Subtract the following:
$ \left(4 x^{2}-\frac{1}{5} x+7\right)-\left(-2 x^{2}-\frac{1}{2} x+\frac{1}{3}\right) $

Given:

\( \left(4 x^{2}-\frac{1}{5} x+7\right)-\left(-2 x^{2}-\frac{1}{2} x+\frac{1}{3}\right) \)

To do:

We have to find the value of \( \left(4 x^{2}-\frac{1}{5} x+7\right)-\left(-2 x^{2}-\frac{1}{2} x+\frac{1}{3}\right) \).

Solution:

$4 x^{2}-\frac{1}{5} x+7-(-2 x^{2}-\frac{1}{2} x+\frac{1}{3})=4x^2-\frac{1}{5}x+7-(-2x^2)-(-\frac{1}{2}x)-\frac{1}{3}$

$=4x^2+2x^2-\frac{1}{5}x+\frac{1}{2}x+7-\frac{1}{3}$

$=6x^2+\frac{-1\times2+1\times5}{10}x+\frac{7\times3-1}{3}$

$=6x^2+\frac{-2+5}{10}x+\frac{21-1}{3}$

$=6x^2+\frac{3}{10}x+\frac{20}{3}$
Therefore,

$4 x^{2}-\frac{1}{5} x+7-(-2 x^{2}-\frac{1}{2} x+\frac{1}{3})=6x^2+\frac{3}{10}x+\frac{20}{3}$.

Tutorialspoint

Updated on: 10-Oct-2022

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