factorise 8 x cube minus 2 x minus y whole cube
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On factoring 8x³ - (2x -y)³ we will get y [ 12x²- 6xy +y² ]
Given:
8x³ - (2x -y)³
To find:
Factorize 8x³ - (2x -y)³
Solution:
Given 8x³ - (2x -y)³
⇒ (2x)³ - (2x -y)³
To factorize above expression 8x³ - (2x -y)³ follow, the following steps
As we know from algebraic identities
a³ - b³ = (a - b) (a² + ab + b²)
Take a = 2x, b = 2x - y and apply above formula
(2x)³ - (2x -y)³ = (2x - 2x + y) [ (2x)² + (2x)(2x -y) + (2x -y)²
= (-y) [ (2x)² + (2x)(2x -y) + (2x -y)² ]
Apply identity [(a - b)² = a²+b²-2ab] on (2x - y)²
= (y) [4x² + 4x²- 2xy + 4x² + y² - 4xy ]
= y [ 12x²- 6xy +y² ]
Therefore,
On factoring 8x³ - (2x -y)³ we will get y [ 12x²- 6xy +y² ]
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