Question

Factorise: 8x³-12x²y+6xy²-y³
please its urgent answer the question step by step
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Answer 1

Answer:

(2x-y)³

Explaination...

8x³ - 12x²y + 6xy² - y³

8x³ - y³ - 12x²y + 6xy²

8x³ - y³ - 8x²y - 4x²y + 2xy² + 4xy²

8x³ - 4x²y - y³ + 2xy² - 8x²y + 4xy²

4x² ( 2x - y ) + y²( -y + 2x ) - 4xy ( 2x - y)

(2x - y) ( 4x² + y² - 4xy)

(2x - y) [(2x)² + (y)² - ( 2 * 2x * y)

(2x - y) ( 2x - y )²

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

Answer 2

Given: The expression $8x^{3} - 12x^2y + 6xy^2 - y^3$is given.

To find: We need to factorize the expression $8x^{3} - 12x^2y + 6xy^2 - y^3$

Solution:

To factorize the expression $8x^{3} - 12x^2y + 6xy^2 - y^3$

We need to apply the concept of taking common terms while simplifying the expression so that it can be written in a more organized way that is,

$8x^3 - 12x^2y + 6xy^2 - y^3\\= 8x^3 - y^3 -12x^2y + 6xy^2\\= 8x^3 - y^3 - 8x^2y - 4x^2y+4xy^2+2xy^2\\= 4x^2(2x-y)+y^2(-y+2x)+4xy(2x-y)\\=(2x-y)(4x^2+y^2+4xy)$

Simplifying the expression $(4x^2+y^2+4xy)$ along with $(2x-y)$ again we get,

$=(2x-y)[(2x)^2+(y)^2-(2*2x*y)]\\=(2x-y)(2x-y)^2\\=(2x-y)^3$

Final answer:

The final expression after factorizing the expression$8x^{3} - 12x^2y + 6xy^2 - y^3$ is$(2x-y)^3$.