Vanessa uses the expression (3x^2+5x+10) and (x^2-3x-1) to represent the length and width of her patio. Which expression represents the area (Iw) of Vanessa's patio?
Accepted Solution
A:
Since you know the length and the width of Vanessa's patio, (3x^2+5x+10) and (x^2-3x-1), to find the expression that represents its area you would multiply the length and width. This would be represented by this expression: (3x^2+5x+10)(x^2-3x-1)
When you multiply the two expressions, you must distribute each term to one another. This would look like this: (3x^2*x^2)+(3x^2*-3x)+(3x^2*-1)+(5x*x^2)+(5x*-3x)+(5x*-1)+(10*x^2)+(10*-3x)+(10*-1)
When simplified, you should get: 3x^4-9x^3-3x^2+5x^3-15x^2-5x+10x^2-30x-10
Then, combine your like terms: 3x^4-4x^3-8x^2-35x-10
Your final answer would be that the expression representing the area of Vanessa's patio is 3x^4-4x^3-8x^2-35x-10