Question

Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
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Answer 1

Area = (3x^2 + 5x + 10)(x^2 − 3x − 1)

Multiply:
3x^2(x^2 − 3x − 1) = 3x^4 − 9x^3 − 3x^2
5x(x^2 − 3x − 1) = 5x^3 − 15x^2 − 5x
10(x^2 − 3x − 1) = 10x^2 − 30x − 10

Add terms:
3x^4 + (−9x^3+5x^3) + (−3x^2−15x^2+10x^2) + (−5x−30x) − 10
= 3x^4 − 4x^3 − 8x^2 − 35x − 10

So the area is 3x^4 − 4x^3 − 8x^2 − 35x − 10.