Question

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

Answer 1

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!