Subtraction of Monomials

Subtracting monomials involves adding the additive inverse of the second monomial to the first.

It requires changing the signs of the terms of the monomial being subtracted and then combining the like terms.

Monomials consist of:

Coefficients: These are constant values like -1, 4, etc.

Variables: These are unknown quantities like x, y, z, etc.

Operators: For subtraction, the operator is the minus (-) symbol.

When subtracting monomials, students should follow these rules:

Flip signs: Always flip the signs of the second monomial and perform addition.

Combine like terms: Only like terms can be subtracted from one another, so group all like terms together.

Simplifying result: After all like terms are combined, the result is typically just the simplified term or zero if exact opposites are subtracted.

The following are the methods for the subtraction of monomials:

Method 1: Horizontal Method

To apply the horizontal method for subtraction of monomials, use the following steps.

Step 1: Write both monomials on the same line using a minus sign in between.

Step 2: Change the signs of the second monomial.

Step 3: Combine the like terms.

Example: Subtract 3x from 5x

Step 1: Write both monomials in the same line, 5x - 3x

Step 2: Change the sign of the second monomial 5x - 3x

Step 3: Combine like terms: Answer: 2x

Method 2: Column Method

When subtracting monomials using the column method, write the monomials one below the other.

Ensure like terms are aligned in each column.

Then change the signs of the second monomial and add the monomials.

Example: Subtract 4x from 7x Solution: Arrange the like terms vertically in columns 7x ← Minuend (from which we subtract) - 4x ← Subtrahend (what we subtract) ----- 3x

Therefore, upon subtracting, we get 3x.

In algebra, subtraction has some characteristic properties.

These properties are listed below:

Subtraction is not commutative In subtraction, changing the order of the terms changes the result, i.e., A - B ≠ B - A

Subtraction is not associative Unlike addition, we cannot regroup in subtraction.

When three or more monomials are involved, changing the grouping changes the result. (A − B) − C ≠ A − (B − C) Subtraction is the addition of the opposite sign

Subtracting a monomial is the same as adding its opposite, so to make calculations easier, you can convert subtraction into addition by changing the signs of the second term.

A − B = A + (−B) Subtracting zero from a monomial leaves the monomial as is Subtracting zero from any monomial results in the same monomial: A - 0 = A

Tips and tricks are useful for students to efficiently deal with the subtraction of monomials. Some helpful tips are listed below:

Tip 1: Always pay attention to signs before combining like terms.

Tip 2: If two monomials have identical terms, they cancel each other out, resulting in zero.

Tip 3: Beginners and visual learners can benefit from using the column method to avoid missing signs and mismatching terms.

Subtraction in algebra is comparatively more challenging than addition, often leading to common mistakes.However, being aware of these errors can help students avoid them.