Question

Which polynomial can be simplified to a difference of squares? 10a2 + 3a – 3a – 16 16a2 – 4a + 4a – 1 25a2 + 6a – 6a + 36 24a2 – 9a + 9a + 4

Answer 1

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

Explanation:

We have to find the polynomial can be simplified to a difference of squares.

1.
`10a^2+3a-3a-16`

Combine like terms

`10a^2-16`

10 in
`10a^2` is not a perfect square number because when a number end with one zero then the number is not perfect square number.

Therefore, it can not be simplified to a difference of squares.

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

`16a^2-1`

Combine like terms

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

Hence, the polynomial can be simplified as difference of squares.

3.
`25a^2+6a-6a+36`

Combine like terms

`25a^2+36`

`(5a)^2+(6)^2`

Hence, the polynomial can not be simplified as difference of squares because the polynomial can be simplified as sum of squares.

4.
`24a^2-9a+9a+4`

Combine like terms

`24a^2+4`

`24a^2+(2)^2`

`24=2* 2* 3* 2`

24 is not a perfect square number because when factorize 24 then 2 and 3 are not paired.

Hence, the polynomial can not be simplified as difference of squares.

Answer 2

16a² - 4a + 4a - 1 can be simplified to a difference of squares:

16a² - 4a + 4a - 1 =
16a² - 1 =
(4a)² - 1² =
(4a-1)(4a+1)