Question

What is the area of a rectangle if one side has a length of `12x^3` and the other side has a width of `6x^2`?

Answer 1

The area of the rectangle is `72x^5`

Explanation:

The formula for the area of a rectangle is:

`A = l xx w`

Where,

`A` is the area, what we are solving for in this problem.

`l` is the length which has been given as `12x^3`

`w` is the width which has been given as `6x^2`

Substituting these values gives:

`A = 12x^3 xx 6x^2`

Simplifying gives:

`A = (12 xx 6) xx (x^3 xx x^2)`

We can multiply the constants and use the rule for exponents to multiply the `x` terms.

`y^color(red)(a) xx y^color(blue)(b) = y^(color(red)(a)+color(blue)(b))`

This gives:

`A = 72 xx (x^(3+2))`

`A = 72 xx x^5`

`A = 72x^5`