Question

How do you multiply `(8x + 3) ( 8x - 3)`?

Answer 1

`64x^2-9`

Explanation:

F.O.I.L

First, Outer, Inner, Last

Multiply the First terms in each set of parenthesis

`8x xx8x=64x^2`

Multiply the Outermost terms in each set of parenthesis

`8x xx -3=-24x`

Multiply the Inner most terms in each set of parenthesis

`3 xx 8x=24x`

Multiply the Last terms in each set or parenthesis

`3xx-3=-9`

`64x^2-24x+24x-9`

Combine like terms

`64x^2-9`

This is DTS, or Difference of Two Squares

Because the first term, `64`, can be square rooted and the last term, `9`, can be square rooted

Answer 2

`(8x+3)(8x-3)=64x^2-9`

Explanation:

`(8x+3)(8x-3)`

This is an example of a difference of squares: `(a^2-b^2)=(a+b)(a-b)`, where `a=8x` and `b=3`.

`(8x)^2-(3^2)`

`64x^2-9`

You could also use the FOIL method, though it is more work. However, you should know both procedures in case your instructor indicates a specific method.

`(8x+3)(8x-3)=8x*8x+8x*-3+3*8x+3*-3`

`(8x+3)(8x-3)=64x^2-24x+24x-9`

`(8x+3)(8x-3)=64x^2-cancel(24x)+cancel(24x)-9`

`(8x+3)(8x-3)=64x^2-9`