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2. Polynomials
hard
નીચેનાના અવયવ પાડો :
$\left(2 x+\frac{1}{3}\right)^{2}-\left(x-\frac{1}{2}\right)^{2}$
Option A
Option B
Option C
Option D
Solution
$\left(2 x+\frac{1}{3}\right)^{2}-\left(x-\frac{1}{2}\right)^{2}$
Using identity $a^{2}-b^{2}=(a+b)(a-b)$
$=\left[\left(2 x+\frac{1}{3}\right)+\left(x-\frac{1}{2}\right)\right]\left[\left(2 x+\frac{1}{3}\right)-\left(x-\frac{1}{2}\right)\right]$
$=\left(2 x+\frac{1}{3}+x-\frac{1}{2}\right)\left(2 x+\frac{1}{3}-x+\frac{1}{2}\right)=\left(3 x-\frac{1}{6}\right)\left(x+\frac{5}{6}\right)$
Standard 9
Mathematics
