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2. Polynomials
medium
સાદુંરૂપ આપો : $(2 x-5 y)^{3}-(2 x+5 y)^{3}$
Option A
Option B
Option C
Option D
Solution
We have,
$(2 x-5 y)^{3}-(2 x+5 y)^{3}$
$=\{(2 x-5 y)-(2 x+5 y)\}\left\{(2 x-5 y)^{2}+(2 x-5 y)(2 x+5 y)+(2 x+5 y)^{2}\right\}$
$\left[\because a^{3}-b^{3}=(a-b)\left(a^{2}+a b+b^{2}\right)\right]$
$=(2 x-5 y-2 x-5 y)\left(4 x^{2}+25 y^{2}-20 x y+4 x^{2}-25 y^{2}+4 x^{2}+25 y^{2}+20 x y\right)$
$=(-10 y)\left(2 x^{2}+25 y^{2}\right)$
$=-120 x^{2} y-250 y^{3}$
Standard 9
Mathematics
