SAT Math: Distribute and use FOIL to expand expressions
41+ practice questions in Praczo
The concept, explained
- 1
To distribute, multiply the term outside a parenthesis by every term inside: a(b + c) = ab + ac. Sign matters — a negative outside flips every inner sign.
- 2
FOIL expands (a + b)(c + d) as First, Outer, Inner, Last: ac + ad + bc + bd. It's just distribution applied to two binomials.
- 3
Be careful with subtraction: (x + 3)(x − 2) = x² − 2x + 3x − 6 = x² + x − 6. Write each signed term explicitly.
- 4
For perfect squares: (a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b². Memorize — the SAT tests these constantly.
- ✗ Forgetting the middle term in (a + b)²: writing it as a² + b² instead of a² + 2ab + b².
- ✗ Dropping a negative sign when distributing into the second binomial term.
SAT-style practice
Which expression is equivalent to (2x − 3)(x + 4)?
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