What is factor 81x^4+25y^2-90x^2y ?

The solution to factor 81x^4+25y^2-90x^2y is (9x^2-5y)^2

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factor 81x^4+25y^2-90x^2y

factor

81 x^{4} + 25 y^{2} - 90 x^{2} y

(9 x^{2} - 5 y)^{2}

Solution steps

81 x^{4} + 25 y^{2} - 90 x^{2} y

Group by common factors

= 81 x^{4} - 90 x^{2} y + 25 y^{2}

Break the expression into groups

= (81 x^{4} - 45 x^{2} y) + (- 45 x^{2} y + 25 y^{2})

Factor out

9 x^{2}

from

81 x^{4} - 45 x^{2} y : 9 x^{2} (9 x^{2} - 5 y)

Factor out

- 5 y

from

- 45 x^{2} y + 25 y^{2} : - 5 y (9 x^{2} - 5 y)

= 9 x^{2} (9 x^{2} - 5 y) - 5 y (9 x^{2} - 5 y)

Factor out common term

9 x^{2} - 5 y

= (9 x^{2} - 5 y) (9 x^{2} - 5 y)

Apply exponent rule:

aa = a^{2}

(9 x^{2} - 5 y) (9 x^{2} - 5 y) = (9 x^{2} - 5 y)^{2}

= (9 x^{2} - 5 y)^{2}

9 - \frac{2}{3}

8 x - 9 y + 16 x + 12 y

(\frac{t ^{3}}{u})^{4}

a^{2} - 6 a + 9 - y^{2}

p^{2} - (r + 2)^{2}

What is factor 81x^4+25y^2-90x^2y ?
The solution to factor 81x^4+25y^2-90x^2y is (9x^2-5y)^2