Factorise- 9x2-2xy-y29

9x^2+2xy+y^29 =(3x)^2 + 2(3x) (y3)+ (y3)^2 =(3x+y3)^2 [∵ a^2+2ab+b^2=(a+b)^2 =(3x+y3)(3x+y3) ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Factorisation Using Algebraic Identities

Factorise: 9x...

Question

Factorise: $9 x^{2} + 2 x y + \frac{y^{2}}{9}$

Open in App

Solution

$9 x^{2} + 2 x y + \frac{y^{2}}{9}$
$= (3 x)^{2} + 2 (3 x) (\frac{y}{3}) + {(\frac{y}{3})}^{2}$
$= {(3 x + \frac{y}{3})}^{2} [∵ a^{2} + 2 a b + b^{2} = (a + b)^{2}$
$= (3 x + \frac{y}{3}) (3 x + \frac{y}{3})$

Suggest Corrections

Similar questions

Factorise by grouping method:

$x^{2} + y^{2} + x + y + 2 x y$

Factorise :

$(i) 2 a^{3} - 50 a (i i) 54 a^{2} b^{2} - 6 (i i i) 64 a^{2} b - 144 b^{3} (i v) (2 x - y)^{3} - (2 x - y) (v) x^{2} - 2 x y + y^{2} - z^{2} (v i) x^{2} - y^{2} - 2 y z - z^{2} (v i i) 7 a^{5} - 567 a (v i i i) 5 x^{2} - \frac{20 x^{4}}{9}$

Q. Which of the following is a factorisation of

9 x^{2} + 2 x y + \frac{y^{2}}{9}

Q. Solve this:

Q1. Factorise

(1) 9x² – 1

(2) 4x⁴ + 12 x³ + 9x²

(3)

\frac{x^{2}}{9} - \frac{y^{2}}{25}

(4)

9 x^{2} + 2 x y + \frac{y^{2}}{9}

Q. Factorise:

9 x^{2} - 6 x y + y^{2} - z^{2}

Join BYJU'S Learning Program

Factorise: 9x2+2xy+y29

9x2+2xy+y29 =(3x)2+2(3x)(y3)+(y3)2 =(3x+y3)2 [∵a2+2ab+b2=(a+b)2 =(3x+y3)(3x+y3)

Factorise: $9 x^{2} + 2 x y + \frac{y^{2}}{9}$

$9 x^{2} + 2 x y + \frac{y^{2}}{9}$
$= (3 x)^{2} + 2 (3 x) (\frac{y}{3}) + {(\frac{y}{3})}^{2}$
$= {(3 x + \frac{y}{3})}^{2} [∵ a^{2} + 2 a b + b^{2} = (a + b)^{2}$
$= (3 x + \frac{y}{3}) (3 x + \frac{y}{3})$