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Factor perfect-square trinomials. Factor the difference of two squares.

Learn how to recognize and factor perfect-square trinomials and differences of two squares with examples and explanations.

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Factor perfect-square trinomials. Factor the difference of two squares.

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  1. Objectives Factor perfect-square trinomials. Factor the difference of two squares.

  2. 3x3x 2(3x2) 22 • • • A trinomial is a perfect square if: • The first and last terms are perfect squares. •The middle term is two times one factor from the first term and one factor from the last term. 9x2 + 12x + 4

  3. Example 1: Recognizing and Factoring Perfect-Square Trinomials Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9x2– 15x + 64

  4. Example 2: Recognizing and Factoring Perfect-Square Trinomials Determine whether each trinomial is a perfect square. If so, factor. If not explain. 81x2 + 90x + 25

  5. Example 3: Recognizing and Factoring Perfect-Square Trinomials Determine whether each trinomial is a perfect square. If so, factor. If not explain. 36x2– 10x + 14

  6. Example 4 Determine whether each trinomial is a perfect square. If so, factor. If not explain. x2 + 4x + 4

  7. Example 5 Determine whether each trinomial is a perfect square. If so, factor. If not explain. x2– 14x + 49

  8. Example 6 Determine whether each trinomial is a perfect square. If so, factor. If not explain. 9x2– 6x + 4

  9. Example 7: Recognizing and Factoring the Difference of Two Squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 3p2– 9

  10. Example 8: Recognizing and Factoring the Difference of Two Squares Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 100x2– 4y2

  11. Example 9 Determine whether each binomial is a difference of two squares. If so, factor. If not, explain. 1 – 4x2

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