Simplifying and Expanding Expressions
Practice combining like terms, distributing, and factoring for PSAT algebra.
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Questions Covered in This Set
11 cards to master
What are like terms?
Terms with the exact same variable part — same letters and same exponents. Only their coefficients differ (e.g., 3x and -7x, or 5xy and -2xy).
Are 4x² and 9x like terms?
No. The exponents differ, so they cannot be combined.
State the distributive property.
a(b + c) = ab + ac — the multiplier reaches every term inside the parentheses.
Simplify 7x - 3 + 2x² - 5x + 8 - x²
x² + 2x + 5 (group: 2x² - x² = x², 7x - 5x = 2x, -3 + 8 = 5)
What does a bare minus sign in front of parentheses mean?
Multiply by -1, so every sign inside flips: -(4x - 9) = -4x + 9.
Simplify 5 - (2x - 3)
8 - 2x (not 5 - 2x - 3; the minus flips both signs)
Simplify 4(2x - 3) - 2(x + 5)
6x - 22 (distribute: 8x - 12 - 2x - 10, then combine)
Expand (x + 3)(x - 5)
x² - 2x - 15 (x(x-5) + 3(x-5) = x² - 5x + 3x - 15)
Factor 12x + 18
6(2x + 3) — pull out the greatest common factor.
What is the plug-in-a-number trick?
Substitute a value like x = 2 or 3 into both expressions; if results differ, they aren't equivalent. Avoid 0 and 1 when possible.
In what order do you handle 3(2x + 1) - (x - 4)?
Distribute first, then combine: 6x + 3 - x + 4 = 5x + 7.
