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?

First lets format the equation correctly

(3x^2 + 5x + 10) (x^2 - 3x - 1)

now we multiply each term on the first parenthesis to all of the terms on the second parenthesis.

so we get

3x^4 + 5x^3 + 10x^2 - 9x^3 - 15x^2 - 30x - 3x^2 - 5x - 10.

then we combine like terms.

3x^4 - 4x^3 - 8x^2 - 35x - 10