Find a pair of factors for each number by using the difference of two squares.

Question

a. 45
b. 77
c. 112

Answer 1

hints:

2²-1²=4-1=3
3²-2²=9-4=5
4²-3²=16-9=7
5²-4²=25-16=9
...
So difference of squares of adjacent integers are odd numbers increasing by 2.

Similarly, difference of adjacent odd or even numbers are multiples of 4 and increase by 4's.
2²-0²=4
3²-1²=8
4²-2²=12
5²-3²=16
6²-4²=20
...