difference of two squares....

Algebra Level 1

Some pair of consecutive integers, $a$ and $b$ , where $a$ is bigger, have sum $7$ . What is $a^2-b^2$ ?

3 solutions

Chew-Seong Cheong
Feb 18, 2020

$a^2-b^2 = (a-b)(a+b) = (1)(7) = \boxed 7$

§Martie On Brilliant
Feb 20, 2020

a + b = 7
Integers are consecutive, therefore a = 4 and b = 3
4² = 16, 3² = 9 ( ² = number multiplied by itself)
16 - 9 = 7 (the answer)

Michael Lee
Feb 20, 2020

a^2-b^2=(a+b)(a-b)

We’re given a+b=7 From the fact that a and b are consecutive we know that their difference is 1. Since a>b it’s a-b=1.

So from above:

a^2+b^2=(a+b)(a-b)=7x1=7