Question

How to factorise = 81x^2+108xy+36y^2

Answer 1

Answer:

Step-by-step explanation:

Using identity (a+b)² = a²+2ab+b²

=> 81x²+108xy+36y2

=> (9x)²+2(9x)(6y)+(6y)²

=> (9x+6y)²

Answer 2

81x² + 108xy + 36y² = 9(3x + 2y)(3x + 2y)

Given :

81x² + 108xy + 36y²

To find :

To factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is 81x² + 108xy + 36y²

Step 2 of 2 :

Factorise the expression

We are aware of the identity that

(a + b)² = a² + 2ab + b²

Using above identity we factorise as below

$\displaystyle \sf 81 {x}^{2} + 108xy + 36 {y}^{2}$

$\displaystyle \sf = 9(9{x}^{2} + 12xy + 4 {y}^{2} )$

$\displaystyle \sf = 9\bigg[{(3x)}^{2} + 2.3x.2y + {(2y)}^{2} \bigg]$

$\displaystyle \sf = 9 {(3x + 2y)}^{2}$

$\displaystyle \sf = 9 (3x + 2y)(3x + 2y)$

∴ 81x² + 108xy + 36y² = 9(3x + 2y)(3x + 2y)

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