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

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

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factor 25y^2-90y+81

factor

25 y^{2} - 90 y + 81

(5 y - 9)^{2}

Solution steps

25 y^{2} - 90 y + 81

Rewrite in the form of

a^{2} + 2 ab + b^{2} :

25 y^{2} = (5 y)^{2}

81 = 9^{2}

- 90 y = - 2 \cdot 5 y \cdot 9

= (5 y)^{2} - 2 \cdot 5 y \cdot 9 + 9^{2}

Apply Perfect Square Formula:

a^{2} - 2 ab + b^{2} = (a - b)^{2}

(5 y)^{2} - 2 \cdot 5 y \cdot 9 + 9^{2} = (5 y - 9)^{2}

= (5 y - 9)^{2}

\frac{1}{2} + (- \frac{5}{2})

\frac{2}{12} + \frac{2}{4}

(x + 1) (x - 1) (x^{2} + 2)

- \frac{1}{4} \cdot 16

- b + b