What is factor 27x^3+64y^6 ?

The solution to factor 27x^3+64y^6 is (3x+4y^2)(9x^2-12xy^2+16y^4)

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factor 27x^3+64y^6

factor

27 x^{3} + 64 y^{6}

(3 x + 4 y^{2}) (9 x^{2} - 12 x y^{2} + 16 y^{4})

Solution steps

27 x^{3} + 64 y^{6}

Apply exponent rules

= (3 x)^{3} + (4 y^{2})^{3}

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(3 x)^{3} + (4 y^{2})^{3} = (3 x + 4 y^{2}) ((3 x)^{2} - 3 x \cdot 4 y^{2} + (4 y^{2})^{2})

= (3 x + 4 y^{2}) ((3 x)^{2} - 3 x \cdot 4 y^{2} + (4 y^{2})^{2})

Simplify

(3 x)^{2} - 3 x \cdot 4 y^{2} + (4 y^{2})^{2} : 9 x^{2} - 12 x y^{2} + 16 y^{4}

= (3 x + 4 y^{2}) (9 x^{2} - 12 x y^{2} + 16 y^{4})

\frac{6 \times 1 0 ^{5}}{2 \times 1 0 ^{3}}

\frac{4 i}{2}

lo g_{\frac{1}{8}} (4)

\frac{0}{i}

What is factor 27x^3+64y^6 ?
The solution to factor 27x^3+64y^6 is (3x+4y^2)(9x^2-12xy^2+16y^4)