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101 LearnersLast updated on August 9, 2025
Math Formula for (a + b - c)²
In mathematics, understanding algebraic identities is crucial for simplifying expressions and solving equations. One such identity is the formula for (a + b - c)². In this topic, we will learn how to expand and use the (a + b - c)² formula.
List of Math Formulas for (a + b - c)²
The (a + b - c)² formula is an algebraic identity used to expand expressions. Let’s learn the formula to expand (a + b - c)².
Math Formula for (a + b - c)²
The formula for (a + b - c)² is derived from the expansion of a binomial expression. It is given by:
(a + b - c)² = a² + 2ab - 2ac + b² - 2bc + c²
Importance of (a + b - c)² Formula
In mathematics, the (a + b - c)² formula helps in simplifying complex algebraic expressions and solving various types of equations. Here are some important aspects of the (a + b - c)² formula.
- It helps in expanding expressions involving three terms efficiently.
- By learning this formula, students can easily understand the concept of expanding and simplifying expressions.
- The formula is also useful in solving quadratic equations and in calculus for differentiating complex functions.
Tips and Tricks to Memorize (a + b - c)² Formula
Students often find algebraic identities tricky and confusing. Here are some tips and tricks to master the (a + b - c)² formula.
- Remember that the square of a sum and difference involves squaring each term and considering the cross-product terms.
- Visualize the formula by breaking it down into smaller parts: square of each term and the double products.
- Practice expanding different expressions using the formula to reinforce memory through application.
Real-Life Applications of (a + b - c)² Formula
The (a + b - c)² formula is used in various real-life applications where expansion of expressions is required. Here are some applications of the (a + b - c)² formula.
- In physics, to calculate the resultant of three forces acting at a point.
- In engineering, to simplify expressions in circuit analysis involving resistance, voltage, and current.
- In computer graphics, for manipulating coordinates in transformations involving translation and rotation.
Common Mistakes and How to Avoid Them While Using (a + b - c)² Formula
Students make errors when expanding (a + b - c)². Here are some common mistakes and ways to avoid them.
Mistake 1
Forgetting the Cross-Product Terms
Students sometimes forget to include the cross-product terms 2ab, -2ac, and -2bc during expansion. To avoid this, remember that each pair of terms from the original expression contributes a product term.
Mistake 2
Incorrect Signs in Expansion
When expanding (a + b - c)², students may get confused with the signs of the cross-product terms. To avoid this, keep track of each term’s sign and carefully apply it during expansion.
Mistake 3
Misplacing Terms
Students sometimes misplace terms or group them incorrectly, leading to errors. Carefully write each step of the expansion to maintain order.
Mistake 4
Confusing (a + b - c)² with Other Identities
Students often confuse this formula with similar-looking identities like (a + b)² or (a - b)². Practice recognizing the difference in structure and terms between these identities.
Mistake 5
Not Simplifying Correctly
After expanding, students may neglect to simplify the expression fully. Always combine like terms and simplify to reach the final expression.
Examples of Problems Using (a + b - c)² Formula
Problem 1
Expand (2 + 3 - 1)².
The expanded form is 16.
Explanation
Using the formula:
(a + b - c)² = a² + 2ab - 2ac + b² - 2bc + c²
where a = 2, b = 3, and c = 1:
(2 + 3 - 1)² = 2² + 2(2)
(3) - 2(2)
(1) + 3² - 2(3)
(1) + 1² = 4 + 12 - 4 + 9 - 6 + 1 = 16
Problem 2
Expand (5 + 4 - 2)².
The expanded form is 81.
Explanation
Using the formula:
(a + b - c)² = a² + 2ab - 2ac + b² - 2bc + c²,
where a = 5, b = 4, and c = 2:
(5 + 4 - 2)² = 5² + 2(5)
(4) - 2(5)
(2) + 4² - 2(4)
(2) + 2² = 25 + 40 - 20 + 16 - 16 + 4 = 81
Problem 3
Expand (6 + 2 - 3)².
The expanded form is 25.
Explanation
Using the formula:
(a + b - c)² = a² + 2ab - 2ac + b² - 2bc + c²,
where a = 6, b = 2, and c = 3:
(6 + 2 - 3)² = 6² + 2(6)
(2) - 2(6)
(3) + 2² - 2(2)
(3) + 3² = 36 + 24 - 36 + 4 - 12 + 9 = 25
Problem 4
Expand (3 + 4 - 5)².
The expanded form is 4.
Explanation
Using the formula:
(a + b - c)² = a² + 2ab - 2ac + b² - 2bc + c²,
where a = 3, b = 4, and c = 5:
(3 + 4 - 5)² = 3² + 2(3)
(4) - 2(3)
(5) + 4² - 2(4)
(5) + 5² = 9 + 24 - 30 + 16 - 40 + 25 = 4
FAQs on (a + b - c)² Formula
1.What is the formula for (a + b - c)²?
2.How is the (a + b - c)² formula derived?
3.What are the applications of the (a + b - c)² formula?
4.Can (a + b - c)² be simplified further after expansion?
Glossary for (a + b - c)² Formula
- Expansion: The process of multiplying out the terms of an expression to remove parentheses.
- Algebraic Identity: An equation that is true for all values of the variables involved.
- Cross-Product Terms: The terms formed by multiplying pairs of different terms in an expression.
- Simplification: The process of reducing an expression to its simplest form.
- Distributive Property: A property that states a(b + c) = ab + ac.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
