Question

Which expressions are equivalent to 16x4 − 64? Check all that apply. 16x4 + 16x – 16x – 64 16x4 – 8x – 8x – 64 (4x2 + 8)(4x2 – 8) 16(x2 + 2)(x2 – 2) 4(4x4 – 8)

Answer 1

16x^4 - 64

equivalent expressions are :
16x^4 + 16x - 16x - 64
(4x^2 + 8)(4x^2 - 8)
16(x^2 + 2)(x^2 - 2)

Answer 2

The given expression is
`16x^(4)-64.`

It can be written as
`16x^(4)+16x-16x-64.`[ we can add or subtract the same thing]

The expression can be factored as difference of two squares

`16x^(4)-64=[4x]^(2)-(8)^(2)=(4x^(2)+8)(4x^(2)-8)`

The common factor of the two terms is 16

WE can take 16 as common factor:
`16x^(4)-64=16[x^(2)-2^(2)]`

=
`16(x^(2)+2)(x^(2)-2)`

Options 1 ,3,4 are the equivalent expressions.