CameraIcon

SearchIcon

MyQuestionIcon

1

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

Addition and Subtraction of Algebraic Expressions

From the sum ...

Question

Question 70

From the sum of $x^{2} - y^{2} - 1, y^{2} - x^{2} - 1$ and $1 - x^{2} - y^{2}$ , subtract $- (1 + y^{2}) .$

Open in App

Solution

Sum of $x^{2} - y^{2} - 1, y^{2} - x^{2} - 1$ and $1 - x^{2} - y^{2}$
$= x^{2} - y^{2} - 1 + y^{2} - x^{2} - 1 + 1 - x^{2} - y^{2}$
On combining the like terms.
$= x^{2} - x^{2} - x^{2} - y^{2} + y^{2} - y^{2} - 1 - 1 + 1 = - x^{2} - y^{2} - 1$
Now, subtract $- (1 + y^{2})$ from $- x^{2} - y^{2} - 1$
$= - x^{2} - y^{2} - 1 - [- (1 + y^{2})] = - x^{2} - y^{2} - 1 + 1 + y^{2} = - x^{2} - y^{2} + y^{2} - 1 + 1 = - x^{2}$

Suggest Corrections

thumbs-up

27

Similar questions

Q. From the sum of

x^{2} - y^{2} - 1, y^{2} - x^{2} - 1

1 - x^{2} - y^{2}

- (1 + y^{2}) .

Question 2 (x)

Add:

$x^{2} - y^{2} - 1, y^{2} - 1 - x^{2}, 1 - x^{2} - y^{2}$

x^{2} + y^{2} + \frac{1}{x^{2}} + \frac{1}{y^{2}} = 4

then the value of

x^{2} + y^{2}

Q. The centres of the circles

x^{2} + y^{2} = 1,

x^{2} + y^{2} + 6 x - 2 y = 1

x^{2} + y^{2} - 12 x + 4 y = 1

Q. Find the angle of intersection of the following curves

(i) y² = x and x² = y
(ii) y = x² and x² + y² = 20
(iii) 2y²= x³ and y² = 32x
(iv) x²+ y² − 4x − 1 = 0 and x² + y² − 2y − 9 = 0
(v)

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

and x² + y² = ab
(vi) x² + 4y² = 8 and x² − 2y² = 2
(vii) x² = 27y and y² = 8x
(viii) x² + y² = 2x and y² = x

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Addition and Subtraction of Algebraic Expressions

Standard VII Mathematics

Join BYJU'S Learning Program

CrossIcon