This document provides algebraic expansions and factorizations of expressions including (a + b)2, (a - b)2, and (x + a)(x + b). It shows that (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (x + a)(x + b) = x2 + (a + b)x + ab.

2. (a + b) 2 = a 2 + ab + ab + b 2 (a + b) 2 = a 2 + 2ab + b 2 b a b a a a b b

3. a a a - b a - b (a – b) 2 (a - b) 2 = a 2 - [b 2 + (ab – b 2 ) + (ab – b 2 ) ] (a - b) 2 = a 2 – [2ab – b 2 ] (a – b 2 ) = a 2 – 2ab + b 2 ab – b 2 b b b 2

4. b a 2 – b 2 = (a + b) (a – b) a a - b a + b a - b

5. x x b b a x x 2 ax bx ab (x + a) (x + b) = x 2 + ax + bx + ab (x + a) (x + b) = x 2 + (a + b)x + ab

6. a b