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Factoring – Special Cases

Factoring – Special Cases. Monday, October 21, 2019. WARM UP. Multiply. (x + 3) (x – 3) (3x – 4)(3x + 4). Perfect Square. Perfect Square. Perfect Square Trinomial. A trinomial is a perfect square if: • The first and last terms are perfect squares.

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Factoring – Special Cases

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  1. Factoring – Special Cases Monday, October 21, 2019

  2. WARM UP • Multiply. • (x + 3) (x – 3) • (3x – 4)(3x + 4)

  3. PerfectSquare Perfect Square Perfect Square Trinomial A trinomial is a perfect square if: • The first and last terms are perfect squares. • Expand (a + b)2 and (a – b)2. • a2 + 2ab + b2 and a2 – 2ab + b2 •The middle term is twice the product of the square roots of the first & last terms . x2 + 8x + 16 ANSWER: (x + 4)2 So , a2 + 2ab + b2 = (a + b)2 AND a2 – 2ab + b2 = (a – b)2

  4. x2 + 2x + 1 (x + 1)2 x2 – 6x + 9 (x – 3)2 x2 – 8x + 64 not a perfect square trinomial 9x2– 15x + 64 not a perfect square trinomial 81x2 + 90x + 25 (9x + 5)2 16x2 + 40x + 25 (4x + 5)2 EX: Tell if the expression is a perfect square. If so, factor it.

  5. Difference of Squares • Expand (a + b)(a – b). • a2 – b2 • This is called a difference of squares.

  6. x2 – 4 (x + 2)(x – 2) x2 – 16 (x – 4)(x + 4) 9x2 – 64 (3x – 8)(3x + 8) x4– 25y6 (x2 + 5y3)(x2– 5y3) 1 – 4x2 (1 + 2x)(1 – 2x) 5x2– 20 EX: Determine whether each binomial is a difference of two squares. If so, factor.

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