Question

Resolve into factors x(x³-y³)-3xy(x-y)

Please step by step explanations​

Answer 1

Answer:

We have, x(x³-y³)-3xy(x-y)

Step 1 -> take x common, = x[ x³-y³ - 3y(x-y) ]

Step 2-> now apply formula of a³-b³ which is equal to (a-b)(a²+ ab + b² )

=>. = x[ (x-y)(x² + xy + y²) - 3y(x-y) ]

Step 3 -> now take x-y common

=>. = x(x-y)[ x² + xy + y² -3y ]

step 4 -> now completing the square of square brackets by adding & subtracting xy

=>. = x(x-y)[ x² + xy + y² + xy -xy -3y ]

=> =x(x-y)( x+y)²( -xy -3y )

step 5-> now take y common from -xy-3y

=>. =x(x-y)( x+y)²(-x-3)y