(x+a)(x+b) Answer

3 min read Jul 03, 2024

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 with x to get x^2
Multiply x with b to get bx
Multiply a with x to get ax
Multiply a with b to get ab

Step 2: Combine like terms

Combine bx and ax to get (a+b)x
Keep x^2 and ab 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.