Question

factorise a cube minus b cube plus b minus a whole cube

Answer 1

Answer:

It’s factoring a difference of Cubes!

a³ - b³ = ( a - b) ( a² + a b + b² )

You see, if you’ll distribute it you’ll get the same answer-

(a - b) ( a² + a b + b² )

a ( a² + a b + b² ) - b ( a² + ab + b² )

a³ + a²b + ab² - a²b -ab² - b³

so by canceling out the positive and negative terms we will get-

a³ - b³

This is the verification process by which you can always check whether you have written the formula correct or not and it would even help you in remembering the formula in an appropriate manner! :)

Note: The quadratic portion of any cube formula do not factor, so don’t waste time attempting to factor it! hehehhe

have a happy Sunday! :)