What is factor 1+18ab+81a^2b^2 ?

The solution to factor 1+18ab+81a^2b^2 is (9ab+1)^2

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factor 1+18ab+81a^2b^2

factor

1 + 18 ab + 81 a^{2} b^{2}

(9 ab + 1)^{2}

Solution steps

1 + 18 ab + 81 a^{2} b^{2}

Group by common factors

= 81 a^{2} b^{2} + 18 ab + 1

Rewrite in the form of

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

81 a^{2} b^{2} = (9 ab)^{2}

1 = 1^{2}

18 ab = 2 \cdot 9 ab \cdot 1

= (9 ab)^{2} + 2 \cdot 9 ab \cdot 1 + 1^{2}

Apply Perfect Square Formula:

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

(9 ab)^{2} + 2 \cdot 9 ab \cdot 1 + 1^{2} = (9 ab + 1)^{2}

= (9 ab + 1)^{2}

(5 x + 7)^{2} = 3

- 4 (v + 4) = 3 (v + 4) + 7

36 + 64

x^{2} = \frac{144}{169}

x^{3} + 3 x^{2} + 3 x + 9

What is factor 1+18ab+81a^2b^2 ?
The solution to factor 1+18ab+81a^2b^2 is (9ab+1)^2