Question

Which expression is a factor of 64x^2−25?

8x−5

32x−25

32x−5

8x−25

Answer 1

Answer:

`(8x-5)^(2)`

Explanation:

Rewrite 64
`x^(2)` as
`(8x)^(2)`

`(8x)^(2)`−80x+25

Rewrite 25 as 5^2.

(8x)^2−80x+5^2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

80x=2⋅(8x)⋅5

Rewrite the polynomial.
`(8x)^2`−2⋅(8x)⋅5+
`5^(2)`

Factor using the perfect square trinomial rule
`a^(2)` −2ab +
`b^(2)`=
`(a-b)^(2)`, where a=8x and b=5.

`(8x-5)^(2)`

Answer 2

A

Explanation: