Question

Factorise:- a²+b²-c²-2ab​

Answer 1

Answer:

$( {a}^{2} - 2ab) \: ( {b}^{2} - {c}^{2} ) \\ a (a - 2b) \: + 1( {b}^{2} - {c}^{2} )$

answer is (a+1) (b^2-c^2)

Answer 2

Answer:

$a^2+b^2-c^2-2ab$  can be factorised as $(a-b-c)(a-b+c)$

Step-by-step explanation:

Firstly, we need to re-arrange the given polynomial as follows

$(a^2+b^2-2ab)-c^2$

Now, if we look at the polynomial inside the bracket, it is the expansion of $(a-b)^2$

Therefore, Substituting the polynomial inside the brackets with $(a-b)^2$ , we get

$(a-b)^2-c^2$

Now, if we look closely, we can observe that the given polynomial is now in form of $x^2-y^2$, so we can apply the following property on it :

$x^2-y^2=(x+y)(x-y)$

So, after applying the property we get

$(a-b-c)(a-b+c)$ which is our required solution.