Question

Factorise : a square minus b square plus 2bc minus c square

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 for factorisation is, a²-b²+2bc-c²

To find : Factorisation of the given algebraic expression.

Solution :

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

We can simply solve this mathematical problem by using the following mathematical process.

Here, we will be using normal algebraic method to perform the given factorisation. (our goal is to do factorisation to the maximum possible extent.)

So,

= a²-b²+2bc-c²

= a²- (b²-2bc+c²)

= a²- (b-c)²

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

(This cannot be further simplified, so this will be considered as the final result.)

Used formulas :

• a²-2ab+b² = (a-b)²
• a²-b² = (a+b) (a-b)

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