Question

Factorise the following :
81x^2-90xy + 25y^2

Answer 1

Answer:

( 9x - 5y ) ( 9x - 5y )

Step-by-step explanation:

Given------> 81 x² - 90 xy + 25y²

To find------> Factors of given expression

Solution-----> 81 x² - 90xy + 25y²

We know that,

81 = 9 × 9

= 9²

25 = 5 × 5

= 5²

90 = 2 × 9 × 5

Now,

81x² - 90xy + 25y²

= 9² x² - 2 × 9 × 5 ( x ) ( y ) + 5² y²

= ( 9x )² - 2 ( 9x ) ( 5y ) + ( 5y )²

We know that,

( a - b )² = a² + b² - 2ab , applying it, we get,

= ( 9x - 5y )²

= ( 9x - 5y ) ( 9x - 5y )

Additional information---->

1) ( a + b )² = a² + b² + 2ab

2) ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

3) ( a² - b² ) = ( a + b ) ( a - b )

4) ( a + b )³ = a³ + b³ + 3ab ( a + b )

5) ( a - b )³ = a³ - b³ - 3ab ( a - b )

Answer 2

81x² - 90xy + 25y² = (9x - 5y)(9x - 5y)

Given :

The expression 81x² - 90xy + 25y²

To find :

To factorise the expression

Formula :

(a - b)² = a² - 2ab + b²

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is 81x² - 90xy + 25y²

Step 2 of 2 :

Factorise the expression

$\displaystyle \sf{ 81 {x}^{2} - 90xy + 25 {y}^{2} }$

$\displaystyle \sf{ = {(9x)}^{2} - 2.9x.5y + {(5y)}^{2} }$

$\displaystyle \sf{ = {(9x - 5y)}^{2}}\: \: \: \bigg[ \: \because \: {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} \bigg]$

$\displaystyle \sf{ = (9x - 5y)(9x - 5y)}$

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