Answer:
[tex](2x+4y)(4x^2-8xy+16y^2)[/tex]
Step-by-step explanation:
We are asked to factor [tex]8x^3+64y^3[/tex].
We can rewrite 8 as [tex]2^3[/tex] and 64 as [tex]4^3[/tex].
[tex](2x)^3+(4y)^3[/tex]
Using sum of cubes [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex], we will get:
[tex](2x)^3+(4y)^3=(2x+4y)((2x)^2-(2x*4y)+(4y)^2)[/tex]
[tex](2x)^3+(4y)^3=(2x+4y)(4x^2-8xy+16y^2)[/tex]
Therefore, the factored form of our given expression would be [tex](2x+4y)(4x^2-8xy+16y^2)[/tex].
