%5E2-formula-expansion.jpeg "(a+b+c)^2 Formula Expansion")
Expanding the Formula: (a+b+c)^2
When dealing with algebraic expressions, expanding formulas is an essential skill to master. One of the most commonly used formulas is the expansion of (a+b+c)^2. In this article, we will explore the step-by-step process of expanding this formula and understand its significance in mathematics.
What is the Formula?
The formula (a+b+c)^2 is a binomial expression raised to the power of 2. It consists of three variables, a, b, and c, added together and then squared.
Expanding the Formula
To expand the formula (a+b+c)^2, we need to follow the rule of exponents, which states that when a binomial is raised to a power, each term in the binomial is raised to that power, and then the terms are multiplied together.
Here's the step-by-step process:
Step 1: Expand the Square
Start by expanding the square of the binomial:
(a+b+c)^2 = (a+b+c) × (a+b+c)
Step 2: Multiply the Terms
Multiply each term in the first binomial with each term in the second binomial:
(a+b+c) × (a+b+c) = a × a + a × b + a × c + b × a + b × b + b × c + c × a + c × b + c × c
Step 3: Simplify the Expression
Simplify the expression by combining like terms:
a × a = a^2
a × b = ab
a × c = ac
b × a = ab (since a × b = b × a)
b × b = b^2
b × c = bc
c × a = ac (since a × c = c × a)
c × b = bc
c × c = c^2
Substitute these simplified expressions into the original equation:
(a+b+c)^2 = a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2
Step 4: Combine Like Terms
Combine like terms to get the final expanded formula:
(a+b+c)^2 = a^2 + 2ab + 2ac + b^2 + 2bc + c^2
And that's it! We have successfully expanded the formula (a+b+c)^2.
Conclusion
Expanding formulas is an essential skill in algebra, and understanding how to expand (a+b+c)^2 is crucial in solving various mathematical problems. By following the step-by-step process outlined above, you should be able to expand this formula with ease. Remember to simplify and combine like terms to get the final expanded formula.
