Table Of Contents

What are the Steps to Subtract Polynomials?

Real-life Applications of Subtracting Polynomials

Common Mistakes and How to Avoid Them in Subtracting Polynomials

Solved Examples of Subtracting Polynomials

FAQs on Subtracting Polynomials

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Last updated on July 5th, 2025

Subtracting Polynomials

Q: What property is used when subtracting polynomials?

While subtracting polynomials, the distributive property is used across the terms of the second polynomial.

Q: How do you simplify the process of subtracting polynomials?

Subtraction of polynomials is a laborious process. However, it can be simplified by using the below mentioned steps: Rearrange the polynomials to get the standard form. Use the distributive property and assign a negative sign to all terms in parentheses of the second polynomial. Combine like terms Simplify the result by adding/subtracting coefficients.

Q: Can we subtract polynomials with different degrees?

Yes, one can do so by aligning like terms and subtracting where possible.

Q: What happens when a variable or exponent is missing?

For a missing term, use zero as the coefficient. This helps in maintaining alignment during subtraction.

Q: What is the difference between the horizontal and vertical method?

Horizontal method Vertical method The polynomials are written in the same line, right next to each other. Polynomials are written one above another. Steps include: Distributing the negative sign, then combining like terms. Steps involved: Align like terms in columns, change signs of the second row, then subtract Preferred for short and simple expressions. Used in longer and more complex polynomial subtractions having multiple terms. It is visually less clear and has a risk of misalignment. It provides visually clear alignments of terms, making subtraction easier. The chances of making sign mistakes are comparatively higher. The chances of sign errors are low due to clarity in alignment. The horizontal method can be used for quick solutions in simple polynomial subtraction. Subtracting polynomials vertically is better when used for complex polynomials as it ensures greater accuracy.

Q: How does learning Algebra help students in United States make better decisions in daily life?

Algebra teaches kids in United States to analyze information and predict outcomes, helping them in decisions like saving money, planning schedules, or solving problems.

Q: How can cultural or local activities in United States support learning Algebra topics such as Subtracting Polynomials?

Traditional games, sports, or market activities popular in United States can be used to demonstrate Algebra concepts like Subtracting Polynomials, linking learning with familiar experiences.

Q: How do technology and digital tools in United States support learning Algebra and Subtracting Polynomials?

At BrightChamps in United States, we encourage students to use apps and interactive software to demonstrate Algebra’s Subtracting Polynomials, allowing students to experiment with problems and see instant feedback for better understanding.

Q: Does learning Algebra support future career opportunities for students in United States?

Yes, understanding Algebra helps students in United States develop critical thinking and problem-solving skills, which are essential in careers like engineering, finance, data science, and more.

Professor Greenline Explaining Math Concepts

A method where the polynomials are subtracted by converting signs to opposites is known as subtracting polynomials. Depending on the expressions, it is similar to addition of polynomials. The positive signs must be changed to negatives and vice versa.

Subtracting Polynomials for US Students

What is Subtracting Polynomials?

Subtraction of polynomials is done using two methods, vertical and horizontal. For simplification, like terms in a polynomial are separated and aligned together. Columns help in matching correct terms during complicated subtractions and this is especially done in the vertical method.

Two rules while subtracting polynomials are:

Like terms should always be together.
The signs of all terms being subtracted must change, i.e., all terms having negative signs changes to positive and vice versa.

What are the Steps to Subtract Polynomials?

Polinomial dikurangkan menggunakan metode vertikal atau metode horizontal. Dalam metode horizontal pengurangan polinomial, tanda-tanda suku yang berada dalam tanda kurung pada ekspresi kedua berubah. Ini menyederhanakan pengurangan sehingga dapat diselesaikan sebagai penjumlahan. Dalam metode vertikal, polinomial disusun dalam kolom satu di atas yang lain berdasarkan suku sejenis. Tanda-tanda kemudian diubah sesuai, dan pengurangan dilanjutkan.

Mari kita pahami langkah-langkah yang digunakan dalam kedua metode:

Metode 1: Metode horizontal

Pastikan polinomial dalam bentuk standar.
Tempatkan polinomial bersebelahan.
Ubah tanda untuk semua suku dalam tanda kurung. Lakukan ini untuk polinomial kedua.
Pisahkan dan susun suku sejenis bersama-sama.
Hitung suku-suku untuk menentukan hasilnya.

Mari kita terapkan langkah-langkah ini pada contoh:

Soal: Kurangkan 2a + 7b -3c dari 6a - 4b + 5c

Karena polinomial sudah dalam bentuk standar, mari kita mulai dengan langkah 2, yaitu menempatkannya secara horizontal.

(6a - 4b + 5c ) - ( 2a + 7b - 3c )

Langkah 3: Ubah tanda
6a - 4b + 5c - 2a - 7b + 3c

Langkah 4: Susun suku sejenis bersama-sama
6a - 2a - 4b - 7b + 5c + 3c

Langkah 5: Selesaikan ekspresi
4a - 11b + 8c

Oleh karena itu, setelah mengurangkan 2a + 7b -3c dari 6a - 4b + 5c, kita mendapat 4a - 11b + 8c.

Metode 2: Metode vertikal

Susun polinomial dalam bentuk standar.
Tempatkan secara vertikal. Suku sejenis ditempatkan satu di atas yang lain.
Dalam kasus suku yang hilang, gunakan 0 sebagai koefisien untuk mempertahankan keselarasan dalam persamaan.
Ubah tanda suku-suku dalam polinomial kedua.
Hitung

Misalnya: Kurangkan 6 + 3x² - 5x dari -2x + 4 - x²

Langkah 1: Susun polinomial dalam bentuk standar

Polinomial pertama : -2x + 4 - x² → -x² - 2x + 4
Polinomial kedua: 6 + 3x² - 5x → 3x² - 5x + 6

Langkah 2: Susun suku sejenis secara vertikal
-x² - 2x + 4
-(3x² - 5x + 6)

Langkah 3: Karena kedua polinomial memiliki suku untuk x², kita tidak perlu menggunakan 0 sebagai koefisien dalam kasus ini.

Langkah 4: Ubah tanda
-x2 - 2x + 4
-3x2 + 5x - 6

Langkah 5: Hitung
(-x² - 3x²) = -4x²
(-2x + 5x) = 3x
(4 - 6) = -2

Oleh karena itu, mengurangkan polinomial yang diberikan secara vertikal, kita mendapat jawaban: -4x² + 3x - 2

Real-life Applications of Subtracting Polynomials

We subtract polynomials to simplify and solve expressions. Subtracting polynomials can also be used to solve real-life situations like:

Calculating usable floor area in architecture

Polynomial subtraction is used to calculate areas. Architects find the usable floor area of staircases, columns, etc., to plan a building's layout accordingly.

Calculating net profit in a business

Business models like revenue and cost have changing values that are modelled as polynomials. The cost model can be subtracted from revenue to find net profit. This process requires polynomial subtraction.

Relative velocity in physics

In motion-related problems, relative velocity is found using polynomial subtraction of velocities of two objects.

Calculating drug concentration in a patient’s body

Pharmacologists use polynomial subtraction to find portions of drugs that have been metabolized in a patient's body over time. This is required for safe drug dosages at regular intervals.

Stock tracking in inventory management

The number of items in stock and sold is expressed as polynomials. Retailers use polynomial subtraction to determine stock levels and make restocking decisions.

Common Mistakes and How to Avoid Them in Subtracting Polynomials

Performing algebraic operations with polynomials can be a little confusing in the beginning. Here are a few common errors related to subtraction of polynomials and how they can be avoided.

Mistake 1

Not changing signs of the second polynomial

Do not forget that the sign of each term of the second polynomial must be changed.

Mistake 2

Combining unlike terms

Combine like terms as unlike terms (x² and x) cannot be combined.

Mistake 3

Errors in rearranging

Pay close attention while writing polynomials in their standard forms and while changing the signs.

Mistake 4

Dropping negative signs

Make sure you don't miss any negative signs while performing calculations.

Mistake 5

Miscalculating arithmetic with coefficients

Do not rush with calculations, check for all signs and coefficients.

Hey!

Solved Examples of Subtracting Polynomials

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Subtract (7x + 4) - (3x - 2)

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Okay, lets begin

4x + 6

Explanation

First, we distribute the negative sign and remove the brackets.

7x + 4 − 3x + 2

Then, we combine the like terms

= (7x − 3x) + (4 + 2)

So, (7x + 4) - (3x - 2) = 4x + 6

Well explained 👍

Problem 2

Subtract (6 + 3x² − 5x) from (−2x + 4 − x²)

Okay, lets begin

−4x² + 3x − 2

Explanation

Step 1: Arrange the polynomials in their standard form

−x² − 2x + 4

3x² − 5x + 6

Step 2: subtract

(−x² − 2x + 4) − (3x² − 5x + 6)

Change signs: −x² −2x + 4 − 3x² + 5x − 6

Combine like terms: (−x² − 3x²) + (−2x + 5x) + (4 − 6) = −4x² + 3x − 2

Well explained 👍

Problem 3

Subtract (5x^3 + 2x²− 4x + 6) − (3x^3 − x² + x−1)

Okay, lets begin

2x³ + 3x² − 5x + 7

Explanation

Distribute the minus sign and remove brackets:

(5x³ + 2x² − 4x + 6) − (3x³+ x² − x + 1)

Group like terms:

(5x³ -3x³) + (2x²+ x²) + (-4 - x) + (6 + 1)

Simplify all terms:

2x³ + 3x² - 5x + 7

Well explained 👍

Problem 4

Subtract (8x^3 + 2 − x) − (5x^3 + 4x)

Okay, lets begin

3x³ − 5x + 2

Explanation

Since neither polynomial has an x² term, use 0 as the coefficient for the missing term i.e., x²:

(8x³ − x + 0x² + 2) − (5x³ + 4x + 0x²+ 0)

Distribute minus: 8x³− x + 2 − 5x³− 4x

Combine the terms: (8x³ − 5x³) + (−x − 4x) + 2 = 3x³− 5x + 2

Well explained 👍

Problem 5

A company's revenue and cost polynomials are: Revenue: R(x) = 4x² + 10x + 100 Cost: C(x) = 3x² + 5x + 60 Find the profit polynomial P(x) = R(x) - C(x)

Okay, lets begin

P(x) = x² + 5x + 40

Explanation

P(x)=(4x² + 10x + 100) − (3x² + 5x + 60)

Change signs: 4x² + 10x + 100 − 3x2 − 5x − 60

Combine like terms: x² + 5x + 40

Well explained 👍

FAQs on Subtracting Polynomials

1.What property is used when subtracting polynomials?

2.How do you simplify the process of subtracting polynomials?

3.Can we subtract polynomials with different degrees?

4.What happens when a variable or exponent is missing?

5.What is the difference between the horizontal and vertical method?

6.How does learning Algebra help students in United States make better decisions in daily life?

7.How can cultural or local activities in United States support learning Algebra topics such as Subtracting Polynomials?

8.How do technology and digital tools in United States support learning Algebra and Subtracting Polynomials?

9.Does learning Algebra support future career opportunities for students in United States?

Explore More algebra

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.