Explain how to find the product of the sum and difference of two terms. Give an example with your explanation.

Given two terms a, b.

Sum of terms = a+b

Difference of terms = a-b

Product of sum and difference (do not forget parentheses)

= (a+b) (a-b)

which can be expanded as=a^2-b^2

We can make use of this property to calculate with lightning speed, assuming you know the squares of numbers.

For example,

8*6 = (7+1) (7-1) = 7^2-1^2=48

9*7 = (8+1 (8-1) = 8^2-1^2=64-1=63

5*15 = (10+5) (10-5) = 10^2-5^2=75

22*18 = (20+2) (20-2) = 20^2-2^2=400-4=396

63*57 = (60+3) (60-3) = 60^2-3^2=3600-9=3591

128*112 = (120+8) (120-8) = 120^2-8^2=14400-64=14336

We can go on and on!