To expand (x − 1)(x + 2)(x + 3), first multiply two brackets: (x + 2)(x + 3) = x² + 5x + 6. Then multiply the result by the third bracket, term by term.
(x − 1)(x² + 5x + 6) = x³ + 5x² + 6x − x² − 5x − 6 = x³ + 4x² + x − 6. For a power like (x − 1)³, write it as three brackets. The answer is a cubic, a polynomial whose highest power is 3.
Worked example
Expand (x − 1)³
- (x − 1)² = x² − 2x + 1.
- (x − 1)(x² − 2x + 1) = x³ − 2x² + x − x² + 2x − 1.
Answer:x³ − 3x² + 3x − 1
Key words
- polynomial
- a sum of powers of x with number coefficients
- cubic
- highest power 3
- term by term
- every term times every term
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Common Core-referenced: HSA-APR.A.1