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.