➕ Algebra 1 · Factoring
Difference of Squares 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 pattern
- a2 − b2 = (a + b)(a − b)
- Needs two perfect squares with a minus sign between them
- The order of the factors does not matter
Perfect squares
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
- Root the number, halve the exponents
- 9y2 = (3y)2 and x6 = (x3)2
- Not squares: x5, 20x2, 7
Steps (FACTS)
- F: GCF First
- A: Are there two squares, one subtracted?
- C: Choose a and b
- T: Two factors (a + b)(a − b)
- S: Spot-check by expanding, Scan for more factoring
Completely factored
- Take out the GCF, then factor every factor you can
- x4 − 16 = (x2 + 4)(x + 2)(x − 2)
- x2 + 4 is prime, so stop there
Limits
- x2 + 9 is prime (not even real coefficients work)
- x2 − 10 does not factor using integers
- (x − 3)2 is x2 − 6x + 9, not x2 − 9
Mental math
- Same distance from a friendly middle number
- 51 × 49 = 502 − 12 = 2499
Formulas
- Difference of squares: a2 − b2 = (a + b)(a − b)
- Expanding the check: (a + b)(a − b) = a2 − ab + ab − b2 = a2 − b2
- Mental math: (n + d)(n − d) = n2 − d2
- A square of a power: (xk)2 = x2k, so halve the exponent to find the root
Difference of Squares cheat sheet from HighSchoolQ.com, for personal study use.