Question

prove that -

a^3-b^3=(a-b) (a^2+ab+b^2)

Correct answer - BRAINLIEST
Incorrect answer - REPORT
And please answer fast
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Answer 1

Answer:

Step-by-step explanation:

Very well known mathematical identity is

(a+b)3=a3+3a2b+3ab2+b3

&

(a−b)3=a3−3a2b+3ab2−b3

The above can be derived easily by successive multiplication like

(a+b)2=(a+b)∗(a+b)

=(a2+a∗b+b∗a+b2)

=(a2+2ab+b2)

So(a+b)3

=(a+b)2∗(a+b)

=(a2+2ab+b2)∗(a+b)

=a3+2a2b+b2a+a2b+2ab2+b3

=a3+3a2b+3ab2+b3

Similar for the other .

Now starting with the second identity

(a−b)3=a3−3a2b+3ab2−b3

Or,(a−b)3+3a2b−3ab2=a3−b3

Or,(a−b)3+3ab(a−b)=a3−b3

Or,(a−b)[(a−b)2+3ab]=a3−b3

Or,(a−b)(a2–2ab+b2+3ab)=a3−b3

Or,(a−b)(a2+ab+b2)=a3−b3

Or,a3−b3=(a−b)(a2+ab+b2)

You can do it from the opposite part like

(a−b)(a2+ab+b2)

=a∗(a2+ab+b2)−b∗(a2+ab+b2)

=a3+a2b+ab2−ba2−ab2−b3

=a3−b3

So

a3−b3=(a−b)(a2+ab+b2)

Answer 2

hii

your answer is given above...

please mark the answer brainliest