Question

factorise 128x⁴y + 250xy⁴​

Answer 1

$Given \: algebraic \: expression :$

$128x^{4}y + 250xy^{4}$

$= \blue{ ( 2xy ) }\times 64x^{3} + \blue{ ( 2xy ) }\times 125y^{3}$

$= 2xy( 64x^{3} + 125y^{3} )$

$= 2xy[ (4x)^{3} + (5y^{3}) ]$

$= 2xy \{ (4x+5y)[(4x)^{2} - (4x)(5y) + (5y)^{2}]\}$

$= 2xy(4x+5y)(16x^{2} - 20xy + 25y^{2})$

Therefore.,

$\red{ Factors \: of \: 128x^{4}y + 250xy^{4} }$

$\green {= 2xy(4x+5y)(16x^{2} - 20xy + 25y^{2})}$

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