Factoring Factoring TrinomialsTrinomialsFactoring Factoring TrinomialsTrinomials

To factor a trinomial squares, use thefollowing relationships.

A2 + 2AB + B2 = (A + B)(A + B)A2 – 2AB + B2 = ( A – B)(A – B)

Factor: 1.) 16a2 – 40ab + 25b2

(4a – 5b)(4a – 5b) (4a – 5b)2

Factor2.) 25x2 – 70x + 49 (5x – 7)(5x – 7) (5x – 7)2

3.) 81x6 + 72x3y + 16y2

(9x3 + 4y)(9x3 + 4y) (9x3 + 4y)2

The Zero Product Principle If the product of two factors is

zero, then one (or both) of the factors must have a value of zero.

If A ∙ B = 0, then A = 0 or B = 0

Example # 17: Solve(a – 10)(2a + 20) = 0 a – 10 = 0 and 2a + 20 = 0 a = 10 2a = - 20 a = - 10Example # 18: Solve x2 – 2x = 35x2 – 2x – 35 = 0(x – 7)(x + 5) = 0 x – 7 = 0 and x + 5 = 0 x = 7 and x = - 5