Question

Factorise
i am not getting how to factorise this one, Can anyone help?
$(a-b)^2-(b-c)^2$

Answer 1

Answer:

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

Step-by-step explanation:

(a-b)² - (b-c)² = a² + b² - 2ab - ( b² + c² - 2bc)

= a² + b² - 2ab - b² - c² + 2bc

= (a² - c²) - (2ab - 2bc)

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

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

Answer 2

Ya sure... Why not...

= (a-b)²-(b-c)²

= (a²+b²-2ab)-(b²-c²+2bc)

= a²-c²-2ab-2bc

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

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