Question

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

Answer 1

Answer:

Step-by-step explanation:

A²+b²-2ab-(b²+c²-2bc)

A²+b²-2ab-b²-c²+2bc

A²-c²-2ab+2bc

A²-c²-2a(b-c)

Answer 2

(a - b)² - (b - c)² = (a - c)(a - 2b + c)

Given :

(a - b)² - (b - c)²

To find :

To factorise the expression

Formula :

a² - b² = (a + b)(a - b)

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

(a - b)² - (b - c)²

Step 2 of 2 :

Factorise the expression

We are aware of the identity that ,

a² - b² = (a + b) (a - b)

Thus we get ,

$\displaystyle \sf{ {(a - b)}^{2} - {(b - c)}^{2} }$

$\displaystyle \sf{ = [(a - b) + (b - c)] \times [(a - b) - (b - c)] }$

$\displaystyle \sf{ = (a - b + b - c) \times (a - b - b + c) }$

$\displaystyle \sf{ = (a - c) (a - 2b + c) }$

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