Question

125x^4 y - 343xy^4 factorise
please tell me step by step ​

Answer 1

$Given \: 125x^{4} y - 343 xy^{4}$

$= xy( 125x^{3} - 343 y^{3})$

$= xy( 5^{3} x^{3} - 7^{3} y^{3} )$

$= xy[(5x)^{3} - (7 y)^{3} ]$

/* By algebraic identity */

$\boxed{ \pink{ a^{3} - b^{3} = (a-b)(a^{2} + ab +b^{2} }}$

$= xy(5x-7y)[ (5x)^{2} + (5x)(7y) + (7y)^{2} ]$

$= xy(5x-7y)(25x^{2} + 35xy+ 49y^{2} )$

Therefore.,

$\red{125x^{4} y - 343 xy^{4}}$

$\green { = xy(5x-7y)(25x^{2} + 35xy+ 49y^{2} ) }$

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