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Term Independent of X

The product o...

Question

The product of $(x^{2} + y^{2}) (x^{2} - y^{2})$ is

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Solution

As we know that $(a + b) (a - b) = a^{2} - b^{2}$
$(x^{2} + y^{2}) (x^{2} - y^{2})$ $= [{(x^{2})}^{2} - {(y^{2})}^{2}]$
$= (x^{4} - y^{4})$
Hence $,$ the product of given algebraic expression is $(x^{4} - y^{4})$

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Similar questions

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

Q. Find the angle of intersection of the following curves:

(i) y² = x and x² = y [NCERT EXEMPLAR]
(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
(ix) y = 4 − x² and y = x² [NCERT EXEMPLAR]

Question 70

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

Q. The product of the rational expressions

\frac{x^{2} - y^{2}}{x^{2} + 2 x y + y^{2}} a n d \frac{x y + y^{2}}{x^{2} - x y}

Q. What should be added to the product of

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

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

x^{2} y^{2}

?

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Term Independent of X

Standard XI Mathematics

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