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Factoring Differences of Squares

Learn how to model and factor polynomials using algebra tiles, focusing specifically on the differences of squares. This guide demonstrates how to handle expressions like (x + 4)(x – 4) and further factors such as x² – 16 and 36x² – 121. We will also cover steps for factoring out common terms, exemplified through 3(x² – 16) and how to simplify them correctly. By practicing with algebra tiles, you can visualize each step, ensuring a solid understanding of the concept of differences of squares and polynomial factoring.

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Factoring Differences of Squares

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  1. Factoring Differences of Squares

  2. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 x - 4

  3. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 Remove the zero pairs. x - 4

  4. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 Remove the zero pairs. x - 4

  5. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 Remove the zero pairs. x - 4

  6. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 Remove the zero pairs. x - 4

  7. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 Remove the zero pairs. x - 4

  8. x2 Model the following problem using algebra tiles: (x + 4)(x – 4) x + 4 Remove the zero pairs. x - 4 What remains is x2 – 16.

  9. Differences of Squares Factor x2 – 64. x2 = x  x 64 = 8  8 x2 – 64 = (x + 8)(x – 8)

  10. Differences of Squares Factor 36x2 – 121. 36x2 = 6x  6x 121 = 11  11 36x2 – 121 = (6x + 11)(6x – 11)

  11. Differences of Squares Factor 3x2-48. First, factor out the three. 3(x2-16) Now factor the difference of the squares. 3(x + 4)(x – 4)

  12. You Try It Factor each polynomial.

  13. Solutions

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