Question

A rectangle has a height of 4x^34x 3 4, x, cubed and a width of x^3+3x^2+2xx 3 +3x 2 +2xx, cubed, plus, 3, x, squared, plus, 2, x. Express the area of the entire rectangle. Your answer should be a polynomial in standard form. A rectangle with a height of 4 X cubed and a width of X cubed plus 3 X squared plus 2 X. The rectangle has 3 sections, one for each term of the width.

Answer 1

`4x^6+12x^5+8x^4`

Explanation:

Height of the rectangle
`=4x^3`

Width of the rectangle
`=x^3+3x^2+2x`

Area of a rectangle = Height X Width

`=4x^3(x^3+3x^2+2x)\\=4x^3*x^3+4x^3*3x^2+4x^3*2x\\=4x^(3+3)+12x^(3+2)+8x^(3+1)\\=4x^6+12x^5+8x^4`

The area of the entire rectangle is:
`4x^6+12x^5+8x^4` in standard form.