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Product Law of Exponent

Simplifya2+b2...

Question

Simplify
$(a^{2} + b^{2}) \times ({- a}^{2} + b^{2}) = ?$

A

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B

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C

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D

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Solution

The correct option is A
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We can write, $- a^{2} + b^{2} = b^{2} - a^{2}$
and $a^{2} + b^{2} = b^{2} + a^{2}$
So, ( $a^{2} + b^{2}) (- a^{2} + b^{2})$
$= (b^{2} + a^{2}) (b^{2} - a^{2})$
$∵ (x + y) (x - y) = (x^{2} - y^{2})$
So, ( $b^{2} + a^{2}) (b^{2} - a^{2})$
$= (b^{2})^{2} - (a^{2})^{2}$
$= b^{4} - a^{4}$

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\frac{\sqrt{a^{2} - b^{2}} + a}{\sqrt{a^{2} + b^{2}} + b} \div \frac{\sqrt{a^{2} + b^{2}} - b}{a - \sqrt{a^{2} - b^{2}}}

(a^{2} b^{2} c^{3} - a^{2} b^{2} c^{3} + a^{2} b^{2} c^{3}) \div a^{2} b^{2} c^{3}

\frac{a + \sqrt{a^{2} - b^{2}}}{a - \sqrt{a^{2} - b^{2}}} + \frac{a - \sqrt{a^{2} - b^{2}}}{a + \sqrt{a^{2} - b^{2}}}

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(a + b)^{2} - 2 a b

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Q. (a²+b²)(-a²+b²)=(b²+a²)(b²-a²) How?

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