An expression is a combination of terms connected by + or − signs. Here are the words you need:
Term
A single number, variable, or combination — separated by + or − signs.
3x is a term. 5 is a term. −2x² is also a term.
In 3x + 5 − 2x² there are three separate terms.
Coefficient
The number in front of the variable. In 3x: coefficient is 3 In −2x²: coefficient is −2 In x: coefficient is 1 (invisible)
Variable
The letter that represents an unknown value. In 5x + 3: the variable is x
Constant
A number with no variable attached. In 4x + 7: the constant is 7
Standard Form: Always write your final answer with the highest exponent first, then work down. 4x² + 3x − 1 is standard form. The GED expects answers written this way.
Step Strategy — How to Simplify
1
Distribute first — if there are parentheses, multiply the outside number by every term inside
2
Identify like terms — same variable, same exponent. Group x² terms, x terms, and constants separately
3
Combine like terms — add or subtract the coefficients, keep the variable the same
4
Write in standard form — highest exponent first
What Are Like Terms?
Like terms have the same variable and the same exponent. You can only combine terms that are alike.
✓ Like Terms — can combine
3x and 7x (both x)
5x² and −2x² (both x²)
4 and 9 (both constants)
✗ NOT Like Terms — cannot combine
3x and 3x² (different exponents)
4x and 4y (different variables)
5x and 5 (one has variable, one doesn't)
Worked Example — Combine Like Terms
Simplify: 4x² + 3x + 2x²
4x² + 3x + 2x²
→ 4x² and 2x² are like terms (both x²)
→ 3x is NOT like x² — different exponent, leave it alone
→ Combine x² terms: 4 + 2 = 6
= 6x² + 3x
Worked Example — Distribute Then Combine
Simplify: −4(x + 2) + 3x
−4(x + 2) + 3x
→ Step 1: Distribute −4 to both terms inside
→ −4 × x = −4x | −4 × 2 = −8 (neg × pos = neg)
−4x − 8 + 3x
→ Step 2: Combine x terms: −4x + 3x = −x
= −x − 8
Common mistakes:
• Combining unlike terms — 3x + x² cannot be simplified
• Forgetting to distribute to ALL terms — −4(x + 2) = −4x − 8, not −4x + 2
• Changing the exponent — 3x + 5x = 8x, not 8x²
🔤 Translating Word Problems into Expressions
The GED often describes an expression in words and asks you to write and simplify it. The key is knowing what each phrase means in math.
Phrase
Math Translation
a number
x
twice a number
2x
3 times a number
3x
3 more than a number
x + 3
3 less than a number
x − 3
5 fewer than a number
x − 5
4 years younger than a number
x − 4
a number increased by 5
x + 5
a number decreased by 5
x − 5
the product of 4 and a number
4x
the sum of a number and 6
x + 6
4 times the sum of x and 3
4(x + 3)
Watch the order for "less than": "3 less than x" = x − 3, NOT 3 − x. The phrase comes after the thing it modifies. This is one of the most common mistakes on the GED.
Worked Example — Translate and Simplify
Write and simplify: twice a number plus 3 more than the same number
→ "twice a number" = 2x
→ "3 more than the same number" = x + 3
2x + x + 3
→ Combine x terms: 2x + x = 3x
= 3x + 3
Worked Example — Translate with Distribution
Write and simplify: 4 times the sum of a number and 3, minus 2 times the number