Question

Which expression is the completely factored form of x3+8y6 ? (x−2y2)(x2+2xy2+4y4) (x+2y2)(x2−2xy2+4y4) (x+2y2)(x2+4y4) (x+2y2)3

Answer 1

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Explanation:

Answer 2

`x^3+8y^6\\\\=x^3+2^3y^(2\cdot3)\\\\=x^3+2^3(y^2)^3\qquad|\text{used}\ (a^n)^m=a^(nm)\\\\=x^3+(2y^2)^3\qquad|\text{used}\ (ab)^n=a^nb^n\\\\=(x+2y^2)(x^2-x\cdot2y^2+(2y^2)^2)\qquad|\text{used}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(x+2y^2)(x^2-2xy^2+2^2(y^2)^2)\\\\=(x+2y^2)(x^2-2xy^2+4y^4)`