Question

Help!!

For what value of x is the value of the square of the binomial 2x +3
is 9 greater than the value of the square of the binomial 2x -3?

Answer 1

x = 3/8

Explanation:

The difference of the two squares can be found several ways. One way uses the "difference of squares" special form.

a² -b² = (a -b)(a +b)

For the given squares, this is ...

(2x +3)² -(2x -3)² = ((2x +3)-(2x -3))((2x +3) +(2x -3)) = 6(4x) = 24x

We want to find x that makes this difference be 9:

24x = 9

x = 9/24 = 3/8

For the value x = 3/8, the difference between the squares of the binomials will be 9.