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16 July, 05:59

1. Find the product (13 - x2) (x + 2).

-x3 - 2x2 + 13x + 26

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Answers (1)
  1. 16 July, 07:09
    0
    The product is - x³ - 2x² + 13x + 26

    Step-by-step explanation:

    * Lets revise how to find the product of two binomials

    - If (ax ± b) and (cx ± d) are two binomials, where a, b, c, d are constant

    their product is:

    # Multiply (ax) by (cx) ⇒ 1st term in the 1st binomial and 1st term in the

    2nd binomial

    # Multiply (ax) by (d) ⇒ 1st term in 1st binomial and 2nd term in

    2nd binomial

    # Multiply (b) by (cx) ⇒ 2nd term in 1st binomial and 1st term in

    2nd binomial

    # Multiply (b) by (d) ⇒ 2nd term in 1st binomial and 2nd term in

    2nd binomial

    # (ax ± b) (cx ± d) = cx² ± adx ± bcx ± bd

    - Add the terms adx and bcx because they are like terms

    * Now lets solve the problem

    - There are two binomials (13 - x²) and (x + 2)

    - We can find their product by the way above

    ∵ (13) (x) = 13x ⇒ 1st term in the 1st binomial and 1st term in the

    2nd binomial

    ∵ (13) (2) = 26 ⇒ 1st term in 1st binomial and 2nd term in

    2nd binomial

    ∵ (-x²) (x) = - x³ ⇒ 2nd term in 1st binomial and 1st term in

    2nd binomial

    ∵ (-x²) (2) = - 2x² ⇒ 2nd term in 1st binomial and 2nd term in

    2nd binomial

    ∴ The product of (13 - x²) (x + 2) = 13x + 26 - x³ - 2x²

    - There is no like terms

    - Lets arrange the terms from greatest power to smallest power

    ∴ The product is - x³ - 2x² + 13x + 26
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