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?

Answer 1

Area = (3x^2 + 5x + 10)(x^2 − 3x − 1)

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

Combine like terms:
Area = 3x^4 − 4x^3 − 8x^2 − 35x − 10