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Simplify (x+9)(x+3)+(x+8)(x+1)

Mathematics

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Answer

2x2+21x+352x^2 + 21x + 35

Step-by-step solution

3 steps

Here's how to simplify the expression using the method shown:

4.2.1 (x+9)(x+3)+(x+8)(x+1)(x+9)(x+3)+(x+8)(x+1)

  1. Find the product of (x+9)(x+3)(x+9)(x+3).

    (x+9)(x+3)=x(x+3)+9(x+3)(x+9)(x+3) = x(x+3) + 9(x+3) =x2+3x+9x+27= x^2 + 3x + 9x + 27 =x2+12x+27(Answer 1)= x^2 + 12x + 27 \quad (\text{Answer 1})

  2. Find the product of (x+8)(x+1)(x+8)(x+1).

    (x+8)(x+1)=x(x+1)+8(x+1)(x+8)(x+1) = x(x+1) + 8(x+1) =x2+x+8x+8= x^2 + x + 8x + 8 =x2+9x+8(Answer 2)= x^2 + 9x + 8 \quad (\text{Answer 2})

  3. Combine Answer 1 and Answer 2, and simplify.

    (x2+12x+27)+(x2+9x+8)(x^2 + 12x + 27) + (x^2 + 9x + 8) =x2+x2+12x+9x+27+8= x^2 + x^2 + 12x + 9x + 27 + 8 =2x2+21x+35= \boxed{2x^2 + 21x + 35}
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