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

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

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factor y^6+27x^3

factor

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

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

Solution steps

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

Apply exponent rules

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

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

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

(x^{2} + 1) \cdot sin (x)

\frac{e ^{t} an x - e ^{s} in x}{( tan ^{2} ( x ) ) ^{3}}

3 x + 8 x^{5} - x + 9 x^{2} - 6 x^{2}

4 (m^{- 1} n)

x^{2} + 13 x y - 30 y^{2}

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