Question

(a+b)^3-(a-b)^3 factorise

Answer 1

Here, [(a+b)^3= a^3+b^3+3ab(a+b)]---------1equation
And next is
[(a-b)^3= a^3-b^3-3ab(a-b)]------------2equation
According to question:
a^3+b^3+3a^2×b+3ab^2-[a^3-b^3-3a^2×b+3ab^2]
a^3+b^3+3a^2×b+3ab^2-a^3+b^3+3a^2×b-3ab^2
= 2b^3+6a^2b answer......
If u can't understand then see this pic.......I hope u will understand...

Answer 2

Answer:

The factorized form of (a+b)³ - (a-b)³ is 2b(3a² + b²).

Step-by-step explanation:

Given - a cubic binomial $(a+b)^3 - (a-b)^3$

To find - Its factorized form

Solution -

We can expand the given binomial into

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

We can group this as
$(a^3+3a^2b+3ab^2+b^3) - (a^3-3a^2b+3ab^2-b^3) = (a^3 - a^3 + 3ab^2 - 3ab^2) + (3a^2b + 3a^2b + b^3 + b^3)$

This can be simplifed as

$(a^3 - a^3 + 3ab^2 - 3ab^2) + (3a^2b + 3a^2b + b^3 + b^3) = 6a^2b + 2b^3$

Which can be further simplified and written as $6a^2b + 2b^3 = 2b(3a^2 + b^2)$

Thus, the factorized form of (a+b)³ - (a-b)³ is 2b(3a² + b²).

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