(2.8) Factoring Special Products OBJECTIVE: To Factor Perfect Square Trinomials and Differences of Squares

Perfect Square Trinomials The squares of binomials a 2 + 2ab + b 2 or a 2 -2ab + b 2 The squares of binomials a 2 + 2ab + b 2 or a 2 -2ab + b 2 Ex: x 2 + 6x + 9 Ex: x 2 - 8x + 16

How Do You Identify Trinomial Squares? The first & last term must be perfect squares. The first and last term must be positive. The middle term is the product of the square roots of the first and last terms times two. The first & last term must be perfect squares. The first and last term must be positive. The middle term is the product of the square roots of the first and last terms times two.

Trinomial Square? x 2 + 6x + 9

Trinomial Square? y 2 + 5y + 25

Trinomial Square? x 2 - 4x + 4

Trinomial Square? a 2 – 7a + 49

Trinomial Square? 4y y + 16

Trinomial Square? 3b 2 – 6b + 1

Factoring Trinomial Squares Work backwards! Use the following equations: a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2 Work backwards! Use the following equations: a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2

Factor as a Trinomial Square: x 2 – 10x + 25 Is this a trinomial square? Are the 1 st & last terms squares? Is the middle term the product of the square roots of the 1 st & last term doubled? Now Work Backwards! Write your parentheses and exponent. Look at the middle term to determine if + or -. Are the 1 st & last terms positive? Take the square root of the 1 st & last terms.

Factor as a Trinomial Square: x 2 – 14x + 49 Is this a trinomial square? Are the 1 st & last terms squares? Is the middle term the product of the square roots of the 1 st & last term doubled? Now Work Backwards! Write your parentheses and exponent. Look at the middle term to determine if + or -. Are the 1 st & last terms positive? Take the square root of the 1 st & last terms.

Factor as a Trinomial Square: y y + 25 Is this a trinomial square? Are the 1 st & last terms squares? Is the middle term the product of the square roots of the 1 st & last term doubled? Now Work Backwards! Write your parentheses and exponent. Look at the middle term to determine if + or -. Are the 1 st & last terms positive? Take the square root of the 1 st & last terms.

Factor as a Trinomial Square: a 2 + 4a - 4 Is this a trinomial square? No, the last term is negative.

Factoring Differences of Squares (a 2 – b 2 ) Work backwards! Use the following equation: a 2 - b 2 = (a + b)(a – b) Write the square root of the 1 st term plus the square root of the 2 nd term, times the square root of the 1 st term minus the square root of the 2 nd term. Work backwards! Use the following equation: a 2 - b 2 = (a + b)(a – b) Write the square root of the 1 st term plus the square root of the 2 nd term, times the square root of the 1 st term minus the square root of the 2 nd term.

Factor : x 2 – 9 Work Backwards! Write your 2 sets of parentheses. Write a + in the 1 st set & a – in the 2 nd set. Write the square roots of the 1 st & last terms in each set.

Factor : y 2 – 4 Work Backwards! Write your 2 sets of parentheses. Write a + in the 1 st set & a – in the 2 nd set. Write the square roots of the 1 st & last terms in each set.

Factor : 25 - a 2 Work Backwards! Write your 2 sets of parentheses. Write a + in the 1 st set & a – in the 2 nd set. Write the square roots of the 1 st & last terms in each set.

Factor : 4x Work Backwards! Write your 2 sets of parentheses. Write a + in the 1 st set & a – in the 2 nd set. Write the square roots of the 1 st & last terms in each set.