Combine like terms to add or subtract polynomials; use the distributive property to multiply!
Polynomial arithmetic uses the same principles as regular arithmetic. ADDING/SUBTRACTING: combine like terms (same variable and exponent). MULTIPLYING: distribute every term of one polynomial to every term of the other — for two binomials, the FOIL method keeps you organized.
(3x² + 2x − 5) + (x² − 4x + 3) = (3x² + x²) + (2x − 4x) + (−5 + 3) = 4x² − 2x − 2
(5x² + 3x − 2) − (2x² − x + 4) Distribute the minus first: = 5x² + 3x − 2 − 2x² + x − 4 = 3x² + 4x − 6
When subtracting, distribute the minus sign to EVERY term inside the parentheses — including the ones that were already negative!
(x + 3)(x − 2) F — First terms: x · x = x² O — Outer terms: x · (−2) = −2x I — Inner terms: 3 · x = 3x L — Last terms: 3 · (−2) = −6 Combine: x² + (−2x + 3x) − 6 = x² + x − 6
What is (x + 5)(x − 3)?
Remember This!
FOIL only works for two binomials × two binomials. For larger polynomials, distribute each term of the first polynomial to every term of the second, then collect like terms.