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3 years ago

Factor: a^2+b^2–c^2+2ab

Mathematics

2 answers:

Kruka [31]3 years ago

6 0

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

Mrac [35]3 years ago

3 0

Answer:

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

Step-by-step explanation:

<u>Use of formula:</u>

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

<u>Factoring the expression</u>

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)

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