Factorise 8xcube-(2x-y)whole cube
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Q. Factorize 8x³ - ( 2x - y )³ .
Solution : 8x³ - ( 2x - y )³
= ( 2x)³ - ( 2x - y )³ { 8x³ = 2x³ · 2x³ · 2x³ = ( 2x )³ }
Let ( 2x ) = A and ( 2x - y ) = B.
= A³ - B³
We know that , ( A³ - B³) = ( A - B ) ( A² + B² + AB )
= ( A - B ) ( A² + B² + AB )
By putting the values of A and B in above step,
= { 2x - ( 2x - y ) } { ( 2x)² + ( 2x - y )² + 2x ( 2x - y ) }
= { 2x - 2x + y } { 4x² + 4x² + y² - 2 · 2x · ( 2x - y ) + 4x² - 2xy }
= ( y ) ( 4x² + 4x² + y² - 8x² + 4xy + 4x² - 2xy )
= ( y ) ( 12x² - 8x² + y² + 4xy - 2xy )
= y ( 4x² + y² + 2xy )
☺☺☺
Q. Factorize 8x³ - ( 2x - y )³ .
Solution : 8x³ - ( 2x - y )³
= ( 2x)³ - ( 2x - y )³ { 8x³ = 2x³ · 2x³ · 2x³ = ( 2x )³ }
Let ( 2x ) = A and ( 2x - y ) = B.
= A³ - B³
We know that , ( A³ - B³) = ( A - B ) ( A² + B² + AB )
= ( A - B ) ( A² + B² + AB )
By putting the values of A and B in above step,
= { 2x - ( 2x - y ) } { ( 2x)² + ( 2x - y )² + 2x ( 2x - y ) }
= { 2x - 2x + y } { 4x² + 4x² + y² - 2 · 2x · ( 2x - y ) + 4x² - 2xy }
= ( y ) ( 4x² + 4x² + y² - 8x² + 4xy + 4x² - 2xy )
= ( y ) ( 12x² - 8x² + y² + 4xy - 2xy )
= y ( 4x² + y² + 2xy )
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