Question

How do you find the product `(2q+5r)(2q-5r)`?

Answer 1

`(2q+5r)(2q-5r)=color(red)(4q^2-25r^2)`

Explanation:

We know (hopefully you remember ...I know I do) that
`color(white)("XXX")(a+b)(a-b)=a^2-b^2` ...this is called "the difference of squares"

In this case using
`color(white)("XXX")2q` in place of `a`, and
`color(white)("XXX")5r` in place of `b`
we have
`(2q+5r)(2q-5r)=(2q)^2-(5r)^2`

`color(white)("XXXXXXXXXXX")=4q^2-25r^2`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Of course, if you don't remember "the difference of squares", you could apply the distributive property:
`(2q+5r)(2q-5r)`
`color(white)("XXX")=2q(2q-5r)+5r(2q-5r)`
`color(white)("XXX")=(2q)^2-(2q)(5r)+(5r)(2q) - (5r)^2`
`color(white)("XXX")=(2q)^2-(5r)^2`
`color(white)("XXX")=4q^2-25r^2`