Factoring Trinomials

To factor a trinomial squares, use the following relationships. A 2 + 2AB + B 2 = (A + B)(A + B) A 2 – 2AB + B 2 = ( A – B)(A – B) Factor: 1.) 16a 2 – 40ab + 25b 2 (4a – 5b)(4a – 5b) (4a – 5b) 2

Factor 2.) 25x 2 – 70x + 49 (5x – 7)(5x – 7) (5x – 7) 2 3.) 81x x 3 y + 16y 2 (9x 3 + 4y)(9x 3 + 4y) (9x 3 + 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 = - 10 Example # 18: Solve x 2 – 2x = 35 x 2 – 2x – 35 = 0 (x – 7)(x + 5) = 0 x – 7 = 0 and x + 5 = 0 x = 7 and x = - 5