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12-72.
  1. Multiply the expressions in parts (a) through (d). Homework Help ✎

    1. (a + b)(a2ab + b2)

    2. (x − 2)(x2 + 2x + 4)

    3. (y + 5)(y2 − 5y + 25)

    4. (xy)(x2 + xy + y2)

    5. What did you notice about these products?

    6. Make up another multiplication problem that will follow the same pattern.

Use a generic rectangle to help you. Pay attention to the negative sign.

a³ + b³

Use the same method as part (a).

Use the same method as part (a).

x³ − 8

Use the same method as part (b).

Look at your final answers. How many terms are there? And what is the largest exponent?

The first factor is a binomial. The second factor is a trinomial. Look for a pattern in the terms of the trinomial. Match the sign pattern in one of the problems. Use a generic rectangle to multiply your factors to be sure you have the pattern.