Question

factorise 8x3-y3-12x2y+6xy2

Answer 1

Answer:

Step-by-step explanation:

8x3-y3-12x2y+6xy2

=(2x)3-(y)3 -3(2x)2(y)+3(2x)(y)2

=(2x-y)3

=(2x-y)(2x-y)(2x-y)

Answer 2

Given,

An algebraic expression: 8x^3-y^3-12x^2y+6xy^2

To find,

The factorization of the given algebraic expression.

Solution,

We can simply solve this mathematical problem using the following process:

As per the algebraic identities;

If a and b are two variables, then,

(a-b)^3

= a^3 - b^3 -3ab(a-b)

= a^3 - b^3 -3a^2b+3ab^2

{Equation-1}

Now,

The given algebraic expression

= 8x^3-y^3-12x^2y+6xy^2

= (2x)^3-(y)^3-3(2x)(y)(2x-y)

= (2x-y)^3

{according to equation-1}

= (2x-y)(2x-y)(2x-y)

Hence, the factorized value of the given algebraic expression is equal to (2x-y)(2x-y)(2x-y).