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Mastering Factoring: Special Cases & Techniques

Dive into the realm of special cases and techniques in factoring algebraic expressions, including perfect squares, trinomials, and differences of squares. Learn to identify, expand, and factor various expressions effectively.

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Mastering Factoring: Special Cases & Techniques

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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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