CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Complex Plane

Simplifyx2+y2...

Question

Simplify
$(x^{2} + y^{2} - \frac{2 x y}{5}) - (- \frac{4 x^{2}}{3} - \frac{4 y^{2}}{5} + \frac{8 x y}{4})$

Open in App

Solution

Consider $= (x^{2} + y^{2} - \frac{2 x y}{5}) - (- \frac{4 x^{2}}{3} - \frac{4 y^{2}}{5} + \frac{8 x y}{4})$
$= x^{2} + y^{2} + \frac{2 x y}{5} + \frac{4 x^{2}}{3} + \frac{4 y^{2}}{5} - \frac{8 x y}{4}$
$= (x^{2} + \frac{4 x^{2}}{3}) + (y^{2} + \frac{4 y^{2}}{5}) + (\frac{2 x y}{5} - \frac{8 x y}{4})$
Taking LCM
$= (\frac{3 x^{2} + 4 x^{2}}{3}) + (\frac{5 y^{2} + 4 y^{2}}{5}) + (\frac{8 x y - 40 x y}{20}) = (\frac{7 x^{2}}{3}) + (\frac{9 y^{2}}{5}) + (\frac{- 32 x y}{20}) = \frac{7 x^{2}}{3} + \frac{9 y^{2}}{5} - \frac{32 x y}{20}$
Hence, $(x^{2} + y^{2} - \frac{2 x y}{5}) - (- \frac{4 x^{2}}{3} - \frac{4 y^{2}}{5} + \frac{8 x y}{4})$ is equal to $\frac{7 x^{2}}{3} + \frac{9 y^{2}}{5} - \frac{32 x y}{20}$

Suggest Corrections

thumbs-up

0

Similar questions

(x^{2} - y^{2} + 2 x y + 1) - (x^{2} + y^{2} + 4 x y - 5)

\frac{x^{2}}{9} - \frac{y^{2}}{4}

\frac{(\sqrt{x})^{\frac{3}{5}} \times (\sqrt{x})^{\frac{2}{5}} + 2 \sqrt{x}}{2 ((\sqrt{x})^{\frac{2}{3}} \times (\sqrt{x})^{\frac{1}{3}}) + \sqrt{x}}

.
(choose two correct alternatives)

\frac{5 + \sqrt{3}}{7 - 4 \sqrt{3}} - \frac{5 - \sqrt{3}}{7 + 4 \sqrt{3}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Geometric Representation and Trigonometric Form

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon