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Factorisation Using Algebraic Identities

xxv Factorise...

Question

Question 92 (xxv)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$16 x^{4} - 625 y^{4}$

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Solution

$16 x^{4} - 625 y^{4} = (4 x^{2})^{2} - (25 y^{2})^{2} = (4 x^{2} + 25 y^{2}) (4 x^{2} - 25 y^{2}) = (4 x^{2} + 25 y^{2}) [(2 x)^{2} - (5 y)^{2}] = (4 x^{2} + 25 y^{2}) (2 x + 5 y) (2 x - 5 y)$

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Factorisation Using Algebraic Identities

Standard VIII Mathematics

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