What happens when you multiply the sum of two quantities by their difference? This calculation occurs so commonly in mathematics that it's worth memorizing a formula. Write the product as (a + b)(a – b).
Now use the FOIL method to multiply the two binomials.
Notice that the middle terms are opposite and add to a zero pair.
So, (a + b)(a + (– b)) = a2 – b2 .
In other words, the product of a + b and a – b is the square of a minus the square of b .
(a + b)(a – b) = a2 – b2
Find the product.
(3x + 4)(3x – 4)
By the Product of a Sum and a Difference, (a + b)(a – b) = a2 – b2 .
Here, a = 3x and b = 4.
(3x + 4)(3x – 4) = (3x)2 – (4)2
(3x + 4)(3x – 4) = 9x2 – 16