Question

Factorise-a2-b2+2bc-c2

Answer 1

a²-b²+2bc-c² =a² - (b² -2bc +c²)
                    =a² - (b-c)²
                    =(a-(b-c))(a+(b-c))  [ using identity a²-b² =(a-b)(a+b) ]
 
                   = (a-b+c)(a+b-c)
hence.,a²-b²+2bc - c²  = (a-b+c)(a+b-c)

Answer 2

Given : The algebraic expression is, a²-b²+2bc-c²

To find : The factorisation of the given algebraic expression.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to factorise the given algebraic expression)

Here, we will be using general algebraic identities in order to factorise the given algebraic expression.

So,

= a²-b²+2bc-c²

= a²- (b²-2bc+c²)

= a² - [(b)² - (2 × b × c) + (c)²]

= a² - (b-c)²

= (a)² - (b-c)²

= (a+b-c) (a-b+c)

(This cannot be further factorised. That's why this will be considered as the final result.)

Used identities :

• x²-2xy+y² = (x-y)²
• x²-y² = (x+y) (x-y)

Hence, the answer to the given factorisation is (a+b-c) (a-b+c)