Question

factorise a-b-a^3+b^3​

Answer 1

Solution

A polynomial is a sum or subtraction between the terms. Factorization is the process of showing the number as a product of the factors.

Here is a suitable identity to factorize the question. Identity refers to some equations that are always satisfied regardless of the number.

• $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$
• $ma+mb=m(a+b)$

The first one is a subtraction of cubes expressed as a product of the factors.

Let's see the last two terms of the question.

→ $-a^{3}+b^{3}$

However, we get $-(a^{3}-b^{3})$ if we factorize it using the second identity.

Let's further factorize.

→ $-(a-b)(a^{2}+ab+b^{2})$

Let's compare with other terms.

→ $a-b$ and $-(a-b)(a^{2}+ab+b^{2})$

We see $a-b$ as a common factor. Factorizing it using the second identity we get the following factorization.

→ $-(a-b)(a^{2}+ab+b^{2}-1)$

Or we can distribute the negative factor in another factor.

→ $\boxed{(b-a)(a^{2}+ab+b^{2}-1)}$

This is our required answer.