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

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)

Answer 2

Answer:

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

Step-by-step 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

$24a^2+4$

$24a^2+(2)^2$

$24=2\times 2\times 3\times 2$

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.