(x%2Bb)(x%2Bc)-formula-expansion.jpeg "(x+a)(x+b)(x+c) Formula Expansion")
Expansion of (x+a)(x+b)(x+c) Formula
The expansion of the formula (x+a)(x+b)(x+c) is a fundamental concept in algebra, and it's essential to understand how to expand it correctly. In this article, we'll dive into the step-by-step process of expanding this formula and explore some examples to illustrate the concept.
The Formula
The formula (x+a)(x+b)(x+c) is a product of three binomials:
(x+a)(x+b)(x+c) = ?
Step-by-Step Expansion
To expand this formula, we need to follow the order of operations (PEMDAS) and multiply each binomial with the other two. Here's the step-by-step process:
Step 1: Multiply (x+a) and (x+b)
(x+a)(x+b) = x^2 + (a+b)x + ab
Step 2: Multiply the result with (x+c)
(x^2 + (a+b)x + ab)(x+c) = ?
Now, let's multiply each term in the first expression with (x+c):
x^2multiplied by(x+c)isx^3 + cx^2(a+b)xmultiplied by(x+c)is(a+b)x^2 + (a+b)cxabmultiplied by(x+c)isabx + abc
Step 3: Combine the terms
Now, let's combine the terms:
x^3 + cx^2 + (a+b)x^2 + (a+b)cx + abx + abc
Simplify the expression
Let's group the like terms together and simplify the expression:
x^3 + (a+b+c)x^2 + (ab+ac+bc)x + abc
And that's the final expanded form of the formula (x+a)(x+b)(x+c)!
Example
Let's consider an example to illustrate the expansion of the formula:
Suppose we want to expand (x+2)(x+3)(x+4). Using the formula, we get:
(x+2)(x+3)(x+4) = x^3 + (2+3+4)x^2 + (2*3+2*4+3*4)x + 2*3*4
Simplifying the expression, we get:
x^3 + 9x^2 + 26x + 24
And that's the expanded form of the given formula!
Conclusion
In this article, we've learned how to expand the formula (x+a)(x+b)(x+c) step-by-step. With practice and patience, you'll become proficient in expanding such formulas and tackling more complex algebraic expressions. Remember to follow the order of operations and multiply each binomial with the other two to get the correct expanded form.
