Factorize : $a^{4} - b^{4}$

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

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

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

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

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Solution

The correct option is B $(a^{2} + b^{2}) (a - b) (a + b)$
$a^{4} - b^{4} = (a^{2})^{2} - (b^{2})^{2}$
Using, $a^{2} - b^{2} = (a + b) (a - b)$
$= (a^{2} + b^{2}) (a^{2} - b^{2})$
Again using, $a^{2} - b^{2} = (a + b) (a - b)$
$(a^{2} + b^{2}) (a + b) (a - b)$

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Similar questions

If X = 1 - a^{2} and Y = 1 - b^{2}, then what is X^{2} + Y^{2} ?

△ A B C

2 a^{2} b^{2} + 2 b^{2} c^{2} = a^{4} + b^{4} + c^{4}, ∠ B =

△ A B C, a^{4} + b^{4} + c^{4} = 2 a^{2} b^{2} + b^{2} c^{2} + 2 c^{2} a^{2},

sin A

The maximum value of the expression $y = 2 (a - x) (x + \sqrt{x^{2} + b^{2}})$ is

a^{4} - 2 a^{2} b^{2} + b^{4}

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