Factor completely. (a^2+2ab+b^2-c^2)
(a+b)^2 - c^2
(a+b+c)(a+b-c)
To factor the expression (a^2 + 2ab + b^2 - c^2) completely, we can use a factoring technique called grouping.
Step 1: Rewrite the expression as a binomial squared minus another squared term:
(a^2 + 2ab + b^2 - c^2) = (a^2 + 2ab + b^2) - c^2
Step 2: Notice that (a^2 + 2ab + b^2) can be factored as a perfect square trinomial:
(a^2 + 2ab + b^2) = (a + b)^2
Step 3: Now, we can rewrite the expression with the factored terms:
(a^2 + 2ab + b^2 - c^2) = (a + b)^2 - c^2
Step 4: Apply the difference of squares formula to factor the expression further:
(a + b)^2 - c^2 = (a + b + c)(a + b - c)
Therefore, the completely factored form of (a^2 + 2ab + b^2 - c^2) is (a + b + c)(a + b - c).