Question

Factorise: 16n2 - 48n + 36 using appropriate identity.​

Answer 1

Answer:

4 (2n + 3)(2n + 3)

Step-by-step explanation:

16n² - 48n + 36

= 4 (4n² + 12n +9)

= 4 (2n + 3)²

= 4 (2n + 3)(2n + 3)

Answer 2

⠀⠀⠀⠀☆ GIVEN⠀ POLYNOMIAL  – 16n² - 48n  + 36 :

⠀⠀⠀⠀

$:\implies\sf 16n^2 -48n + 36 = 0 \\\\\\ \star \sf{By \:Taking\:4\:as\:common\:in\:each \:term\::}\\\\\\ :\implies\sf \cancel {16n^2} -\cancel {48n}+ \cancel {36} = 0\\\\\\ :\implies\sf 4n^2 -12n + 9 = 0\\\\\star \sf{By \:Using\:Sum-Product \:Pattern\::}\\\\ \:\implies\sf 4n^2 -6n -6n + 9 = 0 \\\\\\\star\sf{Finding\:out\:Common\:Terms\::}\\\\\\:\implies\sf 2n(2n - 3) -3(2n - 3) = 0\\\\\\\star\sf{Now,\:Rewrite\:in\:Factored\:term\::}\\\\\\:\implies\sf (2n - 3)\; (2n - 3) = 0\\\\\\:\implies{\underline{\boxed{\frak{\purple{\:\:\:(2n-3)\:\:\ \:\:(2n-3)\:}}}}}\;\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence, \:The\:factors\:are\:\bf{ \:(2n-3)\:\:(2n-3)\:\: }}}}$

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