Question

Can this polynomial be simplified to a difference of squares 16a2 – 4a + 4a – 1

Answer 1

This polynomial can be simplified to a difference of squares

`16a^2 - 4a + 4a - 1=(4a-1)(4a+1)`

Explanation:

Simplify the expression

`16a^2 - 4a + 4a - 1\\\\16a^2- 1`

remember that 4 ^ 2 = 16

Therefore

`16a^2- 1= 4^2a^2 -1`

Remember that

`(4a) ^ 2 = 4 ^ 2a ^ 2`

`4^2a^2 -1=(4a)^2 -1`

As
`1 ^ 2 = 1` then

`(4a)^2 -1= (4a)^2 -1^2`

Remember that
`c ^ 2 -b ^ 2 = (c + b) (c-b)`

In this case
`c = 4a` and
`b = 1`

Finally

`(4a)^2 -1^2 = (4a-1)(4a+1)`