Use the method you discovered in 4.3 to simplify: 4.2.1 (x+9)(x+3)+(x+8)(x+1)

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

Find the product of $(x+9)(x+3)$ .
Multiply the terms using the FOIL method (First, Outer, Inner, Last).
$(x+9)(x+3) = x(x) + x(3) + 9(x) + 9(3)$ $= x^2 + 3x + 9x + 27$ $= x^2 + 12x + 27 \quad (\text{Answer 1})$
Find the product of $(x+8)(x+1)$ .
Multiply the terms using the FOIL method.
$(x+8)(x+1) = x(x) + x(1) + 8(x) + 8(1)$ $= x^2 + x + 8x + 8$ $= x^2 + 9x + 8 \quad (\text{Answer 2})$
Combine the two answers, Answer 1 + Answer 2, and simplify.
Add the results from Step 1 and Step 2.
$(x^2 + 12x + 27) + (x^2 + 9x + 8)$
Combine like terms ( $x^2$ terms, $x$ terms, and constant terms).
$(x^2 + x^2) + (12x + 9x) + (27 + 8)$ $= 2x^2 + 21x + 35$ \boxed{\text{2x^2 + 21x + 35}}
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