Question

How do you multiply `(8x^2+3)(8x^2-3)`?

Answer 1

`64x^4-9`

Explanation:

`color(blue)("Method 1")`

`color(red)((8x^2+3)color(purple)((8x^2-3)))`

Multiply everything inside one bracket by everything inside the other.

`color(purple)(color(red)(8x^2)(8x^2-3)" "color(red)(+3)(8x^2-3))`

`64x^4-24x^2 " "+24x^2-9`

`64x^4 + 0 -9`

`64x^4-9`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Method 2")`
The following is a general equation that is worth committing to memory:

Consider the general case of: `a^2+b^2=(a+b)(a-b)`

Think of `(8x^2+3)(8x^2-3)` as of form `(a+b)(a-b)`

This gives:`" "[(8x^2)^2-3^3] = 64x^4-9 larr" a 1 line solution"`

'..................................................................................
`color(brown)("If this is still not clear then let "u=8x^2" giving:")`

`(u+3)(u-3)=(u^2-3^2)`

But `u=8x^2` giving

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

`=64x^4-9`