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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 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.

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

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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Prove the difference of cubes identity :

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 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, Hence, the proof.

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

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