Factoring Special Products

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Presentation transcript:

Factoring Special Products OBJECTIVE: To Factor Trinomial Squares and Differences of Squares

Trinomial Squares The squares of binomials a2 + 2ab + b2 or a2 -2ab + b2 Ex: x2 + 6x + 9 Ex: x2 - 8x + 16

How Do You Identify Trinomial Squares? The first and 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.

Perfect Square Trinomial? x2 + 6x + 9 Yes!

Perfect Square Trinomial? y2 + 10y - 25 No!

Perfect Square Trinomial? x2 - 4x + 4 Yes!

Perfect Square Trinomial? a2 – 7a + 49 No!

Perfect Square Trinomial? 4y2 + 16y + 16 Yes!

Perfect Square Trinomial? 3b2 – 6b + 1 No!

Factoring Trinomial Squares Work backwards! Use the following equations: a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2

Factor as a Trinomial Square: x2 – 10x + 25 Take the square root of the 1st & last terms. Now Work Backwards! Look at the middle term to determine if + or -. Write your parentheses and exponent.

Factor as a Trinomial Square: x2 – 10x + 25

Factor as a Trinomial Square: x2 – 14x + 49 Take the square root of the 1st & last terms. Now Work Backwards! Look at the middle term to determine if + or -. Write your parentheses and exponent.

Factor as a Trinomial Square: x2 – 14x + 49

Factor as a Trinomial Square: y2 + 10y + 25 Take the square root of the 1st & last terms. Now Work Backwards! Look at the middle term to determine if + or -. Write your parentheses and exponent.

Factor as a Trinomial Square: y2 + 10y + 25

Factor as a Trinomial Square: No, the last term is negative. Is this a trinomial square? a2 + 4a - 4

Factoring Differences of Squares (a2 – b2) Work backwards! Use the following equation: a2 - b2 = (a + b)(a – b) Write the square root of the 1st term plus the square root of the 2nd term, times the square root of the 1st term minus the square root of the 2nd term.

Factor : x2 – 9 Write your 2 sets of parentheses. Work Backwards! Write the square roots of the 1st & last terms in each set. Write a + in the 1st set & a – in the 2nd set .

Factor : x2 – 9

Factor : y2 – 4 Write your 2 sets of parentheses. Work Backwards! Write the square roots of the 1st & last terms in each set. Write a + in the 1st set & a – in the 2nd set .

Factor : y2 – 4

Factor : 25 - a2 Write your 2 sets of parentheses. Work Backwards! Write the square roots of the 1st & last terms in each set. Write a + in the 1st set & a – in the 2nd set .

Factor : 25 - a2

Factor : 4x2 - 81 Write your 2 sets of parentheses. Work Backwards! Write the square roots of the 1st & last terms in each set. Write a + in the 1st set & a – in the 2nd set .

Factor : 4x2 - 81