What is factor w^3y^{12}+1728x^6 ?

The solution to factor w^3y^{12}+1728x^6 is (wy^4+12x^2)(w^2y^8-12wy^4x^2+144x^4)

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factor w^3y^{12}+1728x^6

factor

w^{3} y^{12} + 1728 x^{6}

(w y^{4} + 12 x^{2}) (w^{2} y^{8} - 12 w y^{4} x^{2} + 144 x^{4})

Solution steps

w^{3} y^{12} + 1728 x^{6}

Rewrite

w^{3} y^{12}

(w y^{4})^{3}

Rewrite

1728 x^{6}

(12 x^{2})^{3}

= (w y^{4})^{3} + (12 x^{2})^{3}

Apply Sum of Cubes Formula:

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

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

= (12 x^{2} + w y^{4}) ((12 x^{2})^{2} - 12 x^{2} w y^{4} + (w y^{4})^{2})

Simplify

(w y^{4} + 12 x^{2}) ((w y^{4})^{2} - 12 x^{2} w y^{4} + (12 x^{2})^{2}) : (w y^{4} + 12 x^{2}) (w^{2} y^{8} - 12 w y^{4} x^{2} + 144 x^{4})

= (w y^{4} + 12 x^{2}) (w^{2} y^{8} - 12 w y^{4} x^{2} + 144 x^{4})

+ a c + b c - a d - b d

2 x + x

(x + 1) (x + 2) (x + 3) (x + 4) + 1

\frac{y ^{2} + y}{y ^{2} - 1}

- (4)

What is factor w^3y^{12}+1728x^6 ?
The solution to factor w^3y^{12}+1728x^6 is (wy^4+12x^2)(w^2y^8-12wy^4x^2+144x^4)