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?
I NEED IT SOON PLEASE

Answer 1

Answer:

Area =  $3x^{4} - 4x^{3} - 8x^{2} -35x -10$.

Step-by-step explanation:

Given : Vanessa uses the expressions (3x² + 5x + 10) and (x² – 3x – 1) to represent the length and width of her patio.

To find : Which expression represents the area (lw) of Vanessa’s patio?

Solution : We have given

Length =  (3x² + 5x + 10)

Width =  (x² – 3x – 1)

Area=  length *  width .

Area = (3x² + 5x + 10) *  (x² – 3x – 1).

Area = 3x²  (x² – 3x – 1) + 5x  (x² – 3x – 1) + 10  (x² – 3x – 1).

Area = $3x^{4} - 9x^{3} - 3x^{2} + 5x^{3} - 15x^{2} -5x + 10x^{2} -30x -10$.

Combine like terms

Area =  $3x^{4} - 9x^{3} + 5x^{3} - 3x^{2} - 15x^{2} + 10x^{2} -5x -30x -10$.

Area =  $3x^{4} - 4x^{3} - 18x^{2} + 10x^{2} -35x -10$.

Area =  $3x^{4} - 4x^{3} - 8x^{2} -35x -10$.

Therefore, Area =  $3x^{4} - 4x^{3} - 8x^{2} -35x -10$.

Answer 2

To find the answer to this, you have multiply both expressions by each other. To do this, you have to multiply each term in the first expression by each term in the second expressions. This yields the following: 3x^4-9x^3-3x^2+5x^3-15x^2-5x+10x^2-30x-10. Combing like terms and simplifying gives the final expression: 3x^4 - 4x^3 - 8x^2 - 35x - 10