Question

factorize 9x²+12y-y²-36​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{9x^2+12y-y^2-36}$

$\underline{\textsf{To find:}}$

$\textsf{Factors of}\;\mathsf{9x^2+12y-y^2-36}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{9x^2+12y-y^2-36}$

$\mathsf{=9x^2-(y^2-12y+36)}$

$\mathsf{=(3x)^2-(y-6)^2}$

$\textsf{Using}$

$\boxed{\mathsf{a^2-b^2=(a-b)(a+b)}}$

$\mathsf{=(3x-(y-6))(3x+y-6)}$

$\mathsf{=(3x-y+6)(3x+y-6)}$

$\implies\boxed{\mathsf{9x^2+12y-y^2-36=(3x-y+6)(3x+y-6)}}$

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Answer 2

$Given \: 9x^{2} + 12y - y^{2} - 36$

$= 9x^{2} - y^{2} + 12y - 36$

$= 9x^{2} - (y^{2} - 12y +36)$

$= 9x^{2} - (y^{2} - 2 \times y\times 6 +6^{2})$

/* By algebraic identity */

$\boxed{\pink{ a^{2} - 2ab + b^{2} = (a-b)^{2} }}$

$= 9x^{2} - (y-6)^{2}$

$= (3x)^{2} - (y-6)^{2}$

/* By algebraic identity */

$\boxed{ \blue{ a^{2} - b^{2} = (a+b)(a-b) }}$

$= [3x+(y-6)][3x-(y-6)]$

$= (3x + y - 6 )( 3x - y + 6 )$

Therefore.,

$\red{ Factors \: of \: 9x^{2} + 12y - y^{2} - 36 }$

$\green {= (3x + y - 6 )( 3x - y + 6 ) }$

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