Expansion of (x+a)(x+b)
In algebra, expanding a product of two binomials is a crucial skill. One of the most common examples is expanding the product of (x+a)
and (x+b)
. In this article, we will explore how to expand (x+a)(x+b)
and provide a step-by-step guide to help you master this process.
What is the Expansion of (x+a)(x+b)?
The expansion of (x+a)(x+b)
is given by:
(x+a)(x+b) = x^2 + (a+b)x + ab
This expansion is a result of multiplying each term in the first binomial with each term in the second binomial and then combining like terms.
How to Expand (x+a)(x+b) Step-by-Step
Here's a step-by-step guide to expand (x+a)(x+b)
:
Step 1: Multiply each term in (x+a) with each term in (x+b)
- Multiply
x
withx
to getx^2
- Multiply
x
withb
to getbx
- Multiply
a
withx
to getax
- Multiply
a
withb
to getab
Step 2: Combine like terms
- Combine
bx
andax
to get(a+b)x
- Keep
x^2
andab
as they are
Step 3: Write the final expansion
- The final expansion is
x^2 + (a+b)x + ab
Example: Expanding (x+2)(x+3)
Using the expansion formula, we can expand (x+2)(x+3)
as follows:
(x+2)(x+3) = x^2 + (2+3)x + (2)(3) (x+2)(x+3) = x^2 + 5x + 6
Conclusion
In conclusion, expanding (x+a)(x+b)
is a straightforward process that involves multiplying each term in the first binomial with each term in the second binomial and then combining like terms. By following the step-by-step guide and example provided, you should be able to expand (x+a)(x+b)
with ease.