Question

Factorize :
(i) 125x^3 - 8y^3​

Answer 1

Step-by-step explanation:

We know the formula a^3-b^3 = (a-b)^3-

+3ab(a-b)

Let a=5x, b=2y

So, (5x)^3-(2y)^3 = (5x-2y)^3-3.5x.2y(5x-2y)

=>(5x-2y)-30xy(5x-2y)

It can be also written in the form of a^3-b^3 = (a-b)(a^2+ab+b^2)

so, (5x)^3-(2y)^3 = (5x-2y)(25x^2+10xy+4y^2)

Hope the solution helps!!

Have a good day :-)

Answer 2

Step-by-step explanation:

given:-

$125 {x}^{3} - 8 {y}^{3}$

now as we all know formula

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ \\ we \: apply \: this \: formula \: here \\ \\ \\ ({5x}^{3} ) - ( {2y}^{3} ) \\ \\ (5x - 2y)(25 {x}^{2} + 10xy + 4 {y}^{2} )$