MyQuestionIcon

1

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

Factors of Algebraic Expressions and Factorisation

Simplify x2...

Question

Simplify $\frac{x^{2} + y^{2} - z^{2} + 2 x y}{x^{2} - y^{2} - z^{2} - 2 y z} .$

Open in App

Solution

Simplify $\frac{x^{2} + y^{2} - z^{2} + 2 x y}{x^{2} - y^{2} - z^{2} - 2 y z} = \frac{x^{2} + y^{2} + 2 x y - z^{2}}{x^{2} - [y^{2} + z^{2} + 2 y z]}$
$= \frac{(x + y)^{2} - z^{2}}{x^{2} - (y + z)^{2}} = \frac{((x + y) - z) (x + y + z)}{(x - (y + z)) (x + y + z)}$ $a^{2} - b^{2} = (a - b) (a + b)$
$= \frac{(x + y - z) (x + y + z)}{(x - y - z) (x + y + z)}$
$= \frac{x + y - z}{x - y - z}$

Suggest Corrections

thumbs-up

1

Similar questions

Q. The square root of

x^{2} + y^{2} + z^{2} - 2 x y + 2 y z - 2 z x

\frac{8 (x^{3} y^{2} z^{2} + x^{2} y^{3} z^{2} + x^{2} y^{2} z^{3})}{4 x^{2} y^{2} z^{2}}

Q. Find the sum of

x^{2} + 2 x y + 3 y^{2}, 3 z^{2} + 2 y z + y^{2}, x^{2} + 3 z^{2} + 2 x z, z^{2} - 3 x y - 3 y z

z^{2} - (x^{2} - 2 x y + y^{2})

(x^{2} - 2 x y + y^{2}) - z^{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Factors of Algebraic Expressions and Factorisation

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon