Question

What is the area of a rectangle with a width of x2 + x + 1 and a length of
3x2 - 2x - 1?

Answer 1

`x^(4)` + 3x³ - 3x - 1

Explanation:

The area (A) of a rectangle is calculated as

A = lw ( l is the length and w the width ) , thus

A = (3x² - 2x - 1)(x² + x + 1)

Each term in the second factor is multiplied by each term in the first factor, then

A = 3x²(x² + x + 1) - 2x(x² + x + 1) - 1(x² + x + 1) ← distribute parenthesis

= 3
`x^(4)` + 3x³ + 3x² - 2
`x^(4)` - 2x² - 2x - x² - x - 1 ← collect like terms

=
`x^(4)` + 3x³ - 3x - 1