Section 9.7 “Factor Special Products”

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Presentation transcript:

Section 9.7 “Factor Special Products” (1) perfect square trinomials (2) the difference of two squares Squares are numbers or variables that have a whole number or whole variable square root. x² 9 t² 1 25 4z²

Section 9.7 “Factor Special Products” You can use the following special products patterns to help you factor certain polynomials. Perfect Square Trinomial Pattern (addition) a² + 2ab + b² (a + b)² (a + b)(a + b) Perfect Square Trinomial Pattern (subtraction) a² – 2ab + b² (a – b)² (a - b)(a - b) Difference of Two Squares Pattern a² – b² (a + b)(a – b)

a² + 2ab + b² (a + b)² (x + 5)² x² + 10x + 25 (3x + 2)² 9x² + 12x + 4 Perfect Square Trinomial Pattern (addition) a² + 2ab + b² (a + b)² (a + b)(a + b) Always check for perfect squares FIRST!! (x + 5)² x² + 10x + 25 (3x + 2)² 9x² + 12x + 4 2(3x + 2)² 2(9x² + 12x + 4) 18x² + 24x + 8 Factor out 2 first, then look for perfect squares.

a² – 2ab + b² (a – b)² (x – 3)² x² – 6x + 9 (6y – 1)² 36y² – 12y + 1 Perfect Square Trinomial Pattern (subtraction) a² – 2ab + b² (a – b)² (a - b)(a - b) Always check for perfect squares FIRST!! (x – 3)² x² – 6x + 9 (6y – 1)² 36y² – 12y + 1 3(x² – 2xy + y²) 3x² – 6xy + 3y² 3(x – y)² Factor out 3 first, then look for perfect squares.

a² – b² (a + b)(a – b) x² – 16 (x + 4)(x – 4) 9(2y + 3)(2y – 3) Difference of Two Squares Pattern a² – b² (a + b)(a – b) Always check for perfect squares FIRST!! x² – 16 (x + 4)(x – 4) 9(2y + 3)(2y – 3) 36y² – 81 (7c + d)(7c – d) 49c² – d²