%5E2-formula-expansion.jpeg "(a-b+c)^2 Formula Expansion")
(a-b+c)^2 Formula Expansion
In algebra, when we are dealing with expressions that involve variables and constants, it is often necessary to expand the expression to simplify it or to perform further operations. One such expression is (a-b+c)^2, which can be expanded using the formula for the square of a binomial.
The Formula
The formula for the square of a binomial is given by:
(a+b)^2 = a^2 + 2ab + b^2
In this case, we need to expand (a-b+c)^2, which is not exactly a binomial. However, we can still use the formula by applying it twice.
Step 1: Expand (a-b)^2
First, let's expand (a-b)^2 using the formula:
(a-b)^2 = a^2 - 2ab + b^2
Step 2: Add and Subtract c
Next, we need to add and subtract c to the expression:
(a-b)^2 + c^2 + 2(a-b)c
Step 3: Expand and Simplify
Now, let's expand and simplify the expression:
(a-b)^2 + c^2 + 2(a-b)c = a^2 - 2ab + b^2 + c^2 + 2ac - 2bc
The Final Answer
Therefore, the expansion of (a-b+c)^2 is given by:
(a-b+c)^2 = a^2 - 2ab + b^2 + c^2 + 2ac - 2bc
This formula can be used to expand expressions of the form (a-b+c)^2 in algebra and other branches of mathematics.
