➕ Algebra 1 · Exponents and Polynomials
Multiplying Polynomials cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
Monomials
- Multiply the coefficients, add the exponents of the same variable
- (3x2)(−4x5) = −12x7
- A lone x has exponent 1: x × x3 = x4
- Different variables sit side by side: (2x)(5y) = 10xy
Bigger products
- Every term times every term
- m terms times n terms gives m × n products
- Two binomials: 4 products. Binomial times trinomial: 6 products
- Combine like terms, then write in standard form
Box and FOIL
- Box: one factor across the top, one down the side, one product per cell
- FOIL = First, Outer, Inner, Last, for two binomials only
- (x + 3)(x + 5) = x2 + 5x + 3x + 15 = x2 + 8x + 15
Checks
- Degree of a product = sum of the degrees (nonzero, one variable)
- Test with x = 3 (not 0, 1 or 2)
- A match is a good sign, not a proof
Watch out
- (x + 3)2 means (x + 3)(x + 3), not x2 + 9
- Signs travel with their terms
- Only like terms combine
Formulas
- Monomial times monomial: (axm)(bxn) = (a × b)xm+n
- Monomial times polynomial: a(b + c + d) = ab + ac + ad
- Two binomials: (a + b)(c + d) = ac + ad + bc + bd
- Binomial times trinomial: (a + b)(c + d + e) = ac + ad + ae + bc + bd + be
- Degree of a product: degree of the product = degree of the first factor + degree of the second (both nonzero, one variable)
Multiplying Polynomials cheat sheet from HighSchoolQ.com, for personal study use.