Question

use identity to factorise a² + c² - b² + 2ac​

Answer 1

a^2–2ab+b^2 - c^2

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

(a-b)^2-c^2

Set x =a-b and y=c. The formula becomes

x^2-y^2

factoring this polynomial, we get

(x+y)(x-y)

Substituting back, we get:

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

Let’s multiply it out to check:

A^2 -ab ac

- ab B^2 -bc

-ac bc -c^2

/   QED.

Break it down into parts:

a²+b²-2ab=(a-b)(a-b)

a²+b²-c²-2ab=(a-b)²-c²

Then, factor in c²:

(a-b)²-c²=((a-b)+c)((a-b)-c)

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

HOPE IT HELPS UH