➕ Algebra 1 · Exponents and Polynomials
Special Products of Binomials cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The three patterns
- (a + b)2 = a2 + 2ab + b2
- (a − b)2 = a2 − 2ab + b2
- (a + b)(a − b) = a2 − b2
S-D-S for a binomial squared
- Square the first term
- Double the product of the two terms, each with its own sign
- Square the last term
- Minus sign on the first term: (−4x + 3)2 = 16x2 − 24x + 9
Mental math
- 212 = (20 + 1)2 = 441
- 192 = (20 − 1)2 = 361
- 19 × 21 = 202 − 12 = 399 (same distance each side of 20)
Watch out
- (a + b)2 is not a2 + b2
- (a − b)2 is not a2 − b2
- Last term of (a − b)2 is +b2
- (3x)2 = 9x2
- (x + 3)(x − 5) has no shortcut
Formulas
- Square of a sum: (a + b)2 = a2 + 2ab + b2
- Square of a difference: (a − b)2 = a2 − 2ab + b2
- Sum times difference: (a + b)(a − b) = a2 − b2
- Squares that differ: (a + b)2 − (a − b)2 = 4ab
- Mental-math product: (m − d)(m + d) = m2 − d2
Special Products of Binomials cheat sheet from HighSchoolQ.com, for personal study use.