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Understanding and Factoring Perfect Square Trinomials

This guide focuses on identifying and factoring perfect square trinomials, which take the form of (ax + b)². Learn how to recognize them by checking if both the first and last terms are perfect squares, and whether the middle term fits the pattern of 2 * √(first term) * √(last term). Example problems and practice exercises will help cement your understanding of perfect square trinomials, such as factoring x² - 12x + 36 into (x - 6)². Ideal for students learning algebra, this resource also includes challenging homework to reinforce learning.

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Understanding and Factoring Perfect Square Trinomials

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  1. Warmups – factor. 1) 2xy3 – 6x2y 2) x2 – 12x + 36 3) 4y2 + 36y + 81 4) 4ax – 6bx + 6ay – 9by

  2. 10-5 Perfect Square Trinomials Objective: To identify and factor perfect square trinomials. Standard 11.0

  3. Remember… So….

  4. Recognizing a Perfect Square Trinomial 4x2 + 36xy + 81y2 1st term is a perfect square 3rd term is a perfect square (and positive) 2nd = 2•√1st •√3rd , can be positive or negative Then… Example x2 – 12x + 36 (x – 6)2

  5. TOO: IS IT A PERFECT SQUARE TRINOMIAL? x2 + 8x + 16 x2 + 6x – 9 x2 + 5x + 25 x2 + 10x + 25 4x2 – 20x + 25 x2 + 8x + 12 49 – 14y + y2 2x2 + 8x + 16 x2 – 2x – 3 x2 – 2x + 1 YES NO -9 NO x•2•5 ≠ 5x YES YES NO √12 YES NO 2(x2 + 4x + 8) NO √-3 YES

  6. FACTOR practice time.

  7. Completing the Square Take half of the middle term and square it to get the third term! TOO:

  8. TOO FOR HOMEWORKfactor the perfect square trinomials x2 – 18x + 81 9x2 + 24xy + 16y2 100 + 20x + x2 4x2 + 4x + 1 x2 – 14x + 49

  9. Homework • Perfect Square Trinomials Worksheet

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