Question

a^2 - 2ab + b^2 - c^2
$a {}^{2} - 2ab + b {}^{2} - c {}^{2}$
please solve it
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Answer 1

Required Answer:-

Given to factorise:

• a² - 2ab + b² - c²

Solution:

We know that,

★ (a - b)² = a² - 2ab + b²

Therefore,

a² - 2ab + b² - c²

= [a² - 2ab + b²] - (c)²

= (a - b)² - (c)²

Now, we know that a² - b² = (a + b)(a - b).

Using this identity, we will factorise it.

So,

(a - b)² - (c)²

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

Hence, the factorised form of the polynomial is (a - b + c)(a - b - c)

Answer:

• The factorised form of the polynomial is (a - b + c)(a - b - c).

Answer 2

TO FACTORISE:-

• a²-2ab +b²-c²

Solution:-

a²-2ab+b²-c²

(a²-2ab+b²)-c² //We know (a-b)²=a²+b²-2ab

(a-b)²-c² //Taking (a-b) as (x)

x²-c² //We know a²-b²=(a+b)(a-b)

Therefore,

(x+c)(x-c)

Substituting x....

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

Final answer:-

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