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2. Polynomials
medium
Find the value of
$x^{3}-8 y^{3}-36 x y-216,$ when $x=2 y+6$
A
$1$
B
$6$
C
$0$
D
$-6$
Solution
$x^{3}+8 y^{3}-36 x y-216=x^{3}+(-2 y)^{3}+(-6)^{3}-3 x(-2 y)(-6)$
$=(x-2 y-6)[x^{2}+(-2 y)^{2}+(-6)^{2}-x(-2 y)-(-2 y)(-6)-(-6) x]$
$=(x-2 y-6)\left(x^{2}+4 y^{2}+36+2 x y-12 y+6 x\right)$
$=(0)\left(x^{2}+4 y^{2}+36+2 x y-12 y+6 x\right)=0$ $[\because x=2 y+6]$
Standard 9
Mathematics