Question

Factorize:
$9{(x - 2y)}^{2} - 13 + 4(x - 2y)$
Refer To: NCERT CLASS 9TH
CH-POLYNOMIAL

Answer 1

Method 1 :


9( x - 2y )² - 13 + 4( x - 2y )


→ 9( x - 2y )² + 4( x - 2y ) - 13


→ 9( x - 2y )² + ( 13 - 9 )( x - 2y ) - 13


→ 9( x - 2y )² + 13( x - 2y ) - 9( x - 2y ) - 13


→ ( x - 2y ) { 9( x - 2y ) + 13 } - { 9( x - 2y ) + 13 }


→ { 9( x - 2y ) + 13}{ ( x - 2y - 1 ) }


→ { 9x - 18y + 13 } { x - 2y - 1 }





Method 2 :


Let ( x - 2y ) = a




→ 9a² - 13 + 4a


→ 9a² + 4a - 13


→ 9a² + ( 13 - 9 ) a - 13


→ 9a² + 13a - 9a - 13


→ a( 9a + 13 ) - ( 9a + 13 )


→ ( a - 1 ) ( 9a + 13 )


→ { ( x - 2y ) - 1 } { 9( x - 2y ) + 13 }


→ { x - 2y - 1 } { 9x - 18y + 13 }
$\:$

Answer 2

Method - 1:

Given Equation is 9(x - 2y)^2 + 4(x - 2y) - 13

= > 9(x - 2y)^2 - 9(x - 2y) + 13(x - 2y) - 13

= > 9(x - 2y)[(x - 2y) - 1] + 13[(x - 2y) - 1]

= > [x - 2y - 1][9(x - 2y) + 13]

= > [x - 2y - 1][9x - 18y + 13]

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Method - 2:

Given Equation is 9(x - 2y)^2 + 4(x - 2y) - 13

= > 9(x^2 + 4y^2 - 4xy) + 4x - 8y - 13

= > 9x^2 + 36y^2 - 36xy + 4x - 8y - 13

= > 9x^2 + 36y^2 - 18xy - 18xy - 9x + 13x + 18y - 26y - 13

= > 9x^2 - 18xy - 9x - 18xy + 36y^2 + 18y + 13x - 26y - 13

= > 9x(x - 2y - 1) - 18y(x - 2y - 1) + 13(x - 2y - 1).

= > (x - 2y - 1)(9x - 18y + 13).

Hope this helps!