Maths-
General
Easy

Question

Prove the difference of cubes identity : a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses

Hint:

left parenthesis a minus b right parenthesis left parenthesis c d right parenthesis equals a left parenthesis c d right parenthesis minus b left parenthesis c d right parenthesis where a, b, c and d are real numbers. We are asked to prove the given equation.

The correct answer is: Hence, the proof


    Step 1 of 2:
    The given equation is a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses This can be proved by multiplying the RHS of the equation and simplifying to form the LHS.
    Step 2 of 2:
    Multiply the RHS in the given equation, a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses end cell row cell a cubed minus b cubed equals a open parentheses a squared plus a b plus b squared close parentheses minus b open parentheses a squared plus a b plus b squared close parentheses end cell row cell a cubed minus b cubed equals a cubed plus a squared b plus a b squared minus a squared b minus a b squared minus b cubed end cell row cell a cubed minus b cubed equals a cubed minus b cubed end cell end table
    Hence, the proof.

    To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.

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