Verified answer

16a^3-2y^3 ... Start with the given expression.

2(8a^3-y^3) ... Factor out the GCF 2

2( (2a)^3 - (y)^3 ) ... Rewrite the expression

Since we have a difference of cubes, this means that (2a)^3 - (y)^3 factors to

(2a-y)(4a^2+2ay+y^2). So the final answer is

2(2a-y)(4a^2+2ay+y^2)

So 16a^3-2y^3 completely factors to 2(2a-y)(4a^2+2ay+y^2)

In other words, 16a^3-2y^3 = 2(2a-y)(4a^2+2ay+y^2)

16a^3-2y^3

= 2 ( 8a^3 - y^3 )

= 2 ( (2a)^3 - y^3 )

= 2 Q (4a^2 + 2 a y + y^2)

where Q is the *other* factor in the recipe for "difference of two cubes" which has just been covered in your class. You can also find it by the division algorithm ((8a^3 - ...) / (4 a^2 ...)) that you may have been recently taught.

16a^3-2y^3 = ( (4a^3/2)^2 - ((2y^3)^1/2)^2)

= (4a^3/2 - (2y^3)^1/2) (4a^3/2 + (2y^3)^1/2)