Question

Factor: a^2+b^2–c^2+2ab

Answer 1

Rearrange the polynomial:

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

Answer 2

• (a + b + c)(a + b - c)

Explanation:

Use of formula:

• (a+b)^2 = a^2 + 2ab + b^2
• a^2 - b^2 = (a + b)(a - b)

Factoring the expression

• a^2 + b^2 – c^2 + 2ab =
• (a^2 + 2ab + b^2) - c^2 =
• (a + b)^2 - c^2 =
• (a + b + c)(a + b - c)