Writing and Evaluating Expressions
Substitute numerical values for variables to evaluate algebraic expressions. Practice with multi-variable expressions and real-world formulas like distance = rate × time.
A lesson of Pre-Algebra, in Expressions & Equations, about 10 minutes.
Evaluating and Simplifying Expressions
By the end of this lesson, you will be able to evaluate expressions with multiple variables, apply the distributive property, and combine like terms.
Evaluating with Multiple Variables
Substitute ALL variables, then simplify.
Evaluate $2a - 3b + c$ when $a=5$, $b=2$, $c=-1$:
$2(5) - 3(2) + (-1) = 10 - 6 - 1 = 3$
Evaluate $x^2 + 2xy - y^2$ when $x=3$, $y=-2$:
$9 + 2(3)(-2) - 4 = 9 - 12 - 4 = -7$
The Distributive Property
$$a(b + c) = ab + ac \qquad a(b - c) = ab - ac$$
Expand: $4(3x - 5) = 12x - 20$
$-2(x + 7) = -2x - 14$ (distribute the negative!)
$3(2a + b - 4) = 6a + 3b - 12$
Combining Like Terms
Like terms: same variable AND same exponent.
$3x$ and $7x$ → like (both $x$)
$4x^2$ and $9x$ → NOT like (different exponents)
Combine by adding/subtracting coefficients:
$5x + 3x = 8x$
$7ab - 2ab + ab = 6ab$ (remember: $ab$ has coefficient 1)
$3x^2 + 5x - x^2 + 2 = 2x^2 + 5x + 2$
Putting It Together
Simplify: $4(2x - 3) + 5x - 7$
$= 8x - 12 + 5x - 7$
$= 13x - 19$
Summary
Evaluate: substitute all variables, then use order of operations.
Distributive property: multiply the outside term by every term inside the parentheses.
Like terms: same variable and exponent — add/subtract the coefficients.