Question

Simplify the following expression:
$(ab+bc)(ab-bc)+(bc+ca)(bc-ac)+(ca+ab)(ac-ab)$

• A. -2
• B. 0.0
• C. $2\left[\right(ab{)}^2+(bc{)}^2+(ac{)}^2]$
• D. 2

Answer 1

The correct option is B 0.0

Given expression,
$(ab+bc)(ab-bc)+(bc+ca)(bc-ac)+(ca+ab)(ac-ab)$

Using the identity,
$(a+b)(a-b)=a^2-b^2,$

the given expression can be simplified as
$(ab{)}^2-(bc{)}^2+(bc{)}^2-(ac{)}^2+(ac{)}^2-(ab{)}^2$

By grouping the like terms, this can be further simplified as follows:

$\left[\right(ab{)}^2-\left(ab{)}^2\right]+\left[\right(bc{)}^2-\left(bc{)}^2\right]+\left[\right(ac{)}^2-\left(ac{)}^2\right]=0$