Question

How do you find the product of `(7u+4v)(7u-4v)`?

Answer 1

`(7u+4v)(7u-4v) = 49u^2-16v^2`

Explanation:

You can use the FOIL mnemonic if it helps...

`(7u+4v)(7u-4v) = overbrace((7u)(7u))^"First" + overbrace(color(red)(cancel(color(black)((7u)(-4v)))))^"Outside" + overbrace(color(red)(cancel(color(black)((4v)(7u)))))^"Inside" + overbrace((4v)(-4v))^"Last"`

`color(white)((7u+4v)(7u-4v)) = 49u^2-16v^2`

Alternatively, spot that this is a difference of squares:

`(a+b)(a-b) = a^2-b^2`

with `a=7u` and `b=4v`

Hence:

`(7u+4v)(7u-4v) = (7u)^2-(4v)^2 = 49u^2-16v^2`