Question

Factorize- 1/4(x+y)^2-9/16(x-y)^2​

Answer 1

Solution :

To factorise :

> [ ¼ ( x + y )² ] - [ 9/16 ( x - y )² ]

Each of the terms can be expressed as as square ;

> [ ½ ( x + y ) ]² - [ ¾ ( x - y ) ]² .

The expression , a² - b² can be written as ( a + b )( a - b )

> [ ½ ( x + y ) ]² - [ ¾ ( x - y ) ]² .

> [ ½ ( x + y ) + ¾( x - y) ][ ½( x + y ) - ¾( x - y) ]

> [ ½ x + ½ y + ¾ x - ¾ y ] [ ½ x + ½ y - ¾ x + ¾ y ]

> [ 5/4 x + ¼ y ][ ¼ x + 5/4 y ]

This is the required answer .

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

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

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

Answer:

Required Factorisation :-

At first let make them Square

[½ (x + y)²] - [¾ (x - y)²]

Identity to be used :-

$\sf \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

[ ½ ( x + y ) + ¾( x - y) ][ ½( x + y ) - ¾( x - y) ]

( ½ x + ½ y + ¾ x - ¾ y )( ½ x + ½ y - ¾ x + ¾ y )

(5/4 x + ¼ y )(¼ x + 5/4 y )

Know More :-

(a - b)² = a² - 2ab + b²

(a + b)(a - b) = a² - b²

(a + b)² = a² + 2ab + b²