Question

How do you multiply `(x+4)^3`?

Answer 1

See a solution process below:

Explanation:

We can use Pascal's triangle to solve this problem.

The triangle values for the exponent 3 are:

`1color(white)(.........)3color(white)(.........)3color(white)(.........)1`

Therefore `(x + 4)^3` can be multiplied as:

`(1 xx x^3) + (3 xx 4x^2) + (3 xx 4^2x) + (1 xx 4^3)`

`x^3 + 12x^2 + 48x + 64`

Answer 2

`x^3+12x^2+48x+64`

Explanation:

`"factors of the form"`

`(x+a)(x+b)(x+c)" can be expanded as"`

`x^3+(a+b+c)x^2+(ab+ac+bc)x+abc`

`rArr(x+4)^3=(x+4)(x+4)(x+4)`

`"with " a=b=c=4`

`rArr(x+4)^3`

`=x^3+(4+4+4)x^2+(16+16+16)x+4^3`

`=x^3+12x^2+48x+64`