Question

Factorise x³-125y³-15x²y+75xy²

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Answer 1

Answer:

$(x - 5y) ^{3}$

Step-by-step explanation:

$(x - 5y)^{3}$

Hope it helps you

Answer 2

Given expression:

$x^{3} -125y^{3} -15x^{2} y+75xy^{2}$

$=x^{3} -15x^{2} y +75xy^{2}-125y^{3}$

$=x^{3} + (-5x^{2} y-10x^{2} y)+(50xy^{2} +25xy^{2} )-125y^{3}$

$=x^{3} -5x^{2} y-10x^{2} y+50xy^{2} +25xy^{2} -125y^{3}$

Let us take, '$x^{2}$' common from first two terms, '$-10xy$' common from middle two terms and '$25y^{2}$' from last two terms.

$=x^{2} (x-5y)-10xy(x-5y)+25y^{2} (x-5y)$

Let us take, '$x-5y$' common from the above expression:

$=(x-5y)(x^{2} -10xy+25y^{2} )$

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

Let us take '$x$' common from first two terms and '$-5y$' common from last two terms.

$=[x-5y][x(x-5y)-5y(x-5y)]$

$=[x-5y][(x-5y)(x-5y)]$

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

Hence, $x^{3} -125y^{3} -15x^{2} y+75xy^{2}=(x-5y)^{3}$.