Question

Factorise
(a+b-c) (a-b+c)

Answer 1

Answer: a2−b2+2bc−c2

Step-by-step explanation:

=(a+b+−c)(a+−b+c)

=(a)(a)+(a)(−b)+(a)(c)+(b)(a)+(b)(−b)+(b)(c)+(−c)(a)+(−c)(−b)+(−c)(c)

=a2−ab+ac+ab−b2+bc−ac+bc−c2

=a2−b2+2bc−c2

Answer 2

Que : Factorise (a+b-c) (a-b+c).

Formula used :

1. (a-b)(a+b) = a²-b²

2. (x-y)² = x²-2xy+y²

$\huge\mathbf\red{Solution :}$

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

Using formula → (a-b) (a+b) = a²-b²

= a² - (b-c)²

Using formula → (x-y)² = x²-2xy+y²

= a²- (b²-2bc+c²)

= a² - b² + 2bc - c²

$\boxed{→ a²-b²+2bc-c²}$