Question

Vanessa uses the expressions (3x^2 + 5x + 10) and (x^2 - 3x - 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa's patio?

a. 3x^4 - 4x^3 - 8x^2 - 35x - 10
b. 3x^4 + 14x^3 + 22x^2 + 25x - 10
c. 3x^4 - 4x^3 + 22x^2 + 35x + 10
d. 3x^4 + 14x^3 + 28x^2 + 35x + 10

Answer 1

To find the area of Vanessa's patio, multiply the expressions for length and width and combine like terms, resulting in the expression 3x^4 - 4x^3 - 8x^2 - 35x - 10.

Step-by-step explanation:

Finding the Area of Vanessa's Patio

To find the area of Vanessa's patio, we need to multiply the expressions representing the length and the width. The length is given by (3x^2 + 5x + 10) and the width by (x^2 - 3x - 1). Multiplying these two gives us:

(3x^2 + 5x + 10)(x^2 - 3x - 1) = 3x^4 - 9x^3 - 3x^2 + 5x^3 - 15x^2 - 5x + 10x^2 - 30x - 10

Combining like terms, we get:

• 3x^4
• - 9x^3 + 5x^3 = -4x^3
• - 3x^2 - 15x^2 + 10x^2 = -8x^2
• - 5x - 30x = -35x
• -10

So, the expression representing the area of the patio is 3x^4 - 4x^3 - 8x^2 - 35x - 10.