What is factor 4x^4-12x^2y^3+9y^6 ?

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

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factor 4x^4-12x^2y^3+9y^6

factor

4 x^{4} - 12 x^{2} y^{3} + 9 y^{6}

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

Solution steps

4 x^{4} - 12 x^{2} y^{3} + 9 y^{6}

Break the expression into groups

= (4 x^{4} - 6 x^{2} y^{3}) + (- 6 x^{2} y^{3} + 9 y^{6})

Factor out

2 x^{2}

from

4 x^{4} - 6 x^{2} y^{3} : 2 x^{2} (2 x^{2} - 3 y^{3})

Factor out

- 3 y^{3}

from

- 6 x^{2} y^{3} + 9 y^{6} : - 3 y^{3} (2 x^{2} - 3 y^{3})

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

Factor out common term

2 x^{2} - 3 y^{3}

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

Apply exponent rule:

aa = a^{2}

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

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

64 \cdot \frac{1}{2}

- 4 y - y

- 12 - 18

- x^{2} - x - 1

3 lo g_{7} (343)

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