Virginia SOL Math / Grade 8 / Patterns, Functions & Algebra

8.PFA.1

Equivalent Algebraic Expressions

What you'll learn

  • Simplify algebraic expressions in one variable
  • Apply the distributive property and combine like terms
  • Generate equivalent expressions

Words to know

Term —
a number, variable, or product of them
Coefficient —
the number multiplied by a variable
Like terms —
terms with the same variable and exponent
Distributive property —
a times (b plus c) equals a times b plus a times c
Equivalent expressions —
expressions that are equal for every value of the variable

Why it matters Simplifying expressions makes formulas easier to use and is the first step toward solving equations.

Worked examples

Model ItI do

Simplify 3(x + 4) + 2x.

Distribute the 3: 3x + 12. Then add 2x to get 3x + 2x + 12. Combine like terms: 5x + 12.

Try It TogetherWe do

Simplify 5x - 2(x - 3).

Distribute the -2: -2x + 6. So the expression is 5x - 2x + 6. Combine like terms: 3x + 6.

Now YouYou do

Simplify 4(2x + 1) - 3x.

Distribute, then combine like terms. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Simplify 3x + 4x.

  2. 2.Simplify 2(x + 5).

  3. 3.Simplify 5x + 3 - 2x.

On Level

The core Quick Check from the book.

  1. 1.Simplify 2x + 5x.

  2. 2.Simplify 3(x + 2).

  3. 3.Simplify 6x - 4 + x + 9.

  4. 4.Simplify 2(3x - 1) + 4.

  5. 5.Simplify 7x - 2(x + 5).

Challenge

Stretch your thinking.

  1. 1.Simplify 4(2x - 3) - 2(x - 5).

  2. 2.Simplify 3(x + 2) + 2(2x - 1) - 4.

  3. 3.Write an expression for the perimeter of a rectangle with length (2x + 1) and width (x + 3), simplified.