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Squares and Cubes

Two common factoring situations involve (1) the difference between two squares, and (2) the sum or difference of two cubes.

a2 - b2 = (a + b) (a - b)
a3 + b3 = (a + b) (a2 - ab + b2)
a3 - b3 = (a - b) (a2 + ab + b2)

EX.
y2 - 9 = y2 - 32 = (y + 3) (y - 3)
9t2 - 4 = (3t)2 - 22 = (3t + 2) (3t - 2)
(x + 1)2 - y2 = [(x + 1) + y][(x + 1) - y]

y3 + 8 = y3 + 23 = (y + 2) (y2- 2y + 4)
x3 - 1 = x3 - 13 = (x - 1) (x2+ x + 1)

8s3+ 27 = (2s)3 + 33 = (2s + 3) (4s2- 6s + 9)
64t3 - 125 = (4t)3 - 53 = (4t - 5) (16t2+ 20t + 25)

Subject: 
Algebra
Subject X2: 
Algebra

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