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Maths-

General

Easy

Question

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

The correct answer is: Hence, the proof.

ANSWER:
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 $a comma b comma c$ and d are real numbers.
We are asked to prove the given equation.
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 of the equation, $a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$
$a cubed minus b cubed equals a open parentheses a squared plus a b plus b squared close parentheses minus b open parentheses a squared plus a b plus b squared close parentheses$
$a cubed minus b cubed equals a cubed plus a squared b plus a b squared minus a squared b minus a b squared minus b cubed$
$a cubed minus b cubed equals a cubed minus b cubed$
Hence, the proof.
Note:
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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parallel

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