-(x%2Bb)-answer.jpeg "(x+a) (x+b) Answer")
Expansion of (x+a) (x+b)
In algebra, the expansion of a product of two binomials, such as (x+a) and (x+b), is a fundamental concept. In this article, we will explore the step-by-step process of expanding the product (x+a) (x+b) and discuss the resulting expression.
Step-by-Step Expansion
To expand the product (x+a) (x+b), we need to multiply each term in the first binomial with each term in the second binomial. This process is often referred to as the distributive property of multiplication over addition.
Multiply x with each term in the second binomial
- x * x = x^2
- x * b = bx
Multiply a with each term in the second binomial
- a * x = ax
- a * b = ab
Combine like terms
Now, let's combine the resulting terms from the multiplication:
x^2 + bx + ax + ab
Simplified Expression
By combining like terms, we can simplify the expression further:
x^2 + (b+a)x + ab
This is the final expanded form of the product (x+a) (x+b).
Conclusion
In conclusion, the expansion of (x+a) (x+b) is a simple yet important concept in algebra. By following the step-by-step process outlined above, we can easily derive the resulting expression, which is x^2 + (b+a)x + ab. This expression is useful in various mathematical applications, including solving quadratic equations and graphing quadratic functions.
