Lesson 7: Simplify Algebraic Expressions

Property

The identity property of addition: for any real number $a$,

$0$ is called the additive identity.

The identity property of multiplication: for any real number $a$,

$1$ is called the multiplicative identity.

Examples

• The expression $42 + 0$ simplifies to $42$ by the identity property of addition.
• Using the identity property of multiplication, the expression $1 \cdot (-5y)$ simplifies to $-5y$.
• When simplifying $0 + (x+y)$, the identity property of addition shows the result is just $x+y$.

Property

Like terms are terms where the variable part is the same. The numbers multiplied by the variable are called the coefficients.

To add or subtract like terms:

1. Add or subtract the coefficients.
2. Do not change the variable part of the terms.

Examples

• To combine $8m - 3m$, we subtract the coefficients: $(8-3)m = 5m$.
• To combine $7ab + 5ab$, we add the coefficients: $(7+5)ab = 12ab$.
• To combine $y + 9y$, remember the coefficient of $y$ is 1. So, $(1+9)y = 10y$.