X^4 y^4 by x^2 y^2 x^4 y^4 = (x^2)^2 (y^2)^2 =(x^2 + y^2)(x^2 y^2) ∴x^4 y^4/x^2 y^2 = (x^2 + y^2 )(x^2 y^2)/x^2 y^2 = x^2 + y^2 ...

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Division of a Polynomial by a Polynomial

x4 - y4 by x...

Question

Divide $x^{4} - y^{4}$ by $x^{2} - y^{2}$ .

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Solution

Given $(x^{4} - y^{4}) \div (x^{2} - y^{2})$
Since, we have $a^{2} - b^{2} = (a - b) (a + b)$ .......(i)
Substitute $a = x^{2}$ and $b = y^{2}$ in equation(i), we get
$(x^{2})^{2} - (y^{2})^{2} = (x^{2} - y^{2}) (x^{2} + y^{2})$
$\Rightarrow (x^{4} - y^{4}) = (x^{2} - y^{2}) (x^{2} + y^{2})$ ......(ii)
Now substitute equation(ii) in given expression.
$\frac{(x^{4} - y^{4})}{(x^{2} - y^{2})} = \frac{(x^{2} - y^{2}) (x^{2} + y^{2})}{(x^{2} - y^{2})}$
$= x^{2} + y^{2}$
Hence, the value of the given expression is $= x^{2} + y^{2}$

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Similar questions

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

(x^{4} - y^{4}) : (x + y)^{4}

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

x^{4} + x^{2} y^{2} + y^{4}

Factorize

i) x⁴ - y⁴+ x²- y²

x^{4} + x^{2} y^{2} + y^{4}

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