Question

factories the polynomial: 8x^3-(2x-y)^3​

Answer 1

Given, 8x^3 - (2x - y) ^3

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

Using the formula:

a^3 - b^3= (a - b)(a^2 + ab + b^2) -------- eq.(1)

Putting the value of a = 2x, b = (2x – y) in the above formula; we get

= (2x – (2x+y)) {(2x) ^2 - 2x*(2x - y) + (2x - y) ^2}

= y {(4x^2 - 4x^2 + 2xy + 4x^2 - 4xy + y^2)}

= y (4x^2 - 2xy + y^2)

Therefore, factorized form of the given problem is y (4x^2 - 2xy + y^2).

$\small\mathfrak\red{Hope \: you \: have \: satisfied}$

Answer 2

Answer:

Given, 8x^3 - (2x - y) ^3

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

Using the formula:

a^3 - b^3= (a - b)(a^2 + ab + b^2) ----1

Giving values of a = 2x, b = (2x – y) in the above formula; we get

= (2x – (2x+y)) {(2x) ^2 - 2x*(2x - y) + (2x - y) ^2}

= y {(4x^2 - 4x^2 + 2xy + 4x^2 - 4xy + y^2)}

= y (4x^2 - 2xy + y^2)

= 4x^2 - 2xy + y^2