Question

what is the product of (7x+6)(7x-6)

Answer 1

49x^2-36 you multiply them together like a normal multiplication problem.

Answer 2

There is a short way and a long way to do it.

The long way is to distribute one of these, and keep distributing.

For example, let u = 7x+6. Then our expression is u(7x-6) = u*7x - u*6.

Now I substitute u back in: (7x+6)(7x) - (7x+6)(6)
= (49x^2 + 42x) - (42x + 36)
= 49x^2 + 42x - 42x - 36 <- careful distributing the negative!
= 49x^2 - 36.

So what's the short way? Recognize this is in the form of a difference of perfect squares.
(a-b)(a+b) = a^2 - b^2.

In our case a = 7x, and b = 6.

So a^2 - b^2 = (7x)^2 - 6^2 = 49x^2 - 36!