(a+b)(a+c) Formula

3 min read Jul 03, 2024

Algebraic Formula: (a+b)(a+c)

In algebra, the formula (a+b)(a+c) is a fundamental concept that is widely used in various mathematical operations. This formula represents the product of two binomials, where each binomial consists of two terms.

What is the Formula?

The formula (a+b)(a+c) can be expanded as:

(a+b)(a+c) = a^2 + ac + ab + bc

This formula is obtained by multiplying each term in the first binomial (a+b) with each term in the second binomial (a+c).

How to Apply the Formula?

To apply the formula, follow these steps:

Multiply the first term in the first binomial (a) with each term in the second binomial (a+c).
- a × a = a^2
- a × c = ac
Multiply the second term in the first binomial (b) with each term in the second binomial (a+c).
- b × a = ab
- b × c = bc
Combine the four terms obtained in steps 1 and 2 to get the final result.

Example

Let's apply the formula to a simple example:

(x+2)(x+3)

Using the formula, we get:

(x+2)(x+3) = x^2 + 3x + 2x + 6

Combine like terms:

(x+2)(x+3) = x^2 + 5x + 6

Applications

The (a+b)(a+c) formula has numerous applications in various fields, including:

Algebraic equations: to solve quadratic equations and systems of equations.
Geometry: to calculate the area and perimeter of shapes, such as rectangles and triangles.
Calculus: to find the derivative and integral of functions.

Conclusion

In conclusion, the (a+b)(a+c) formula is a powerful tool in algebra that helps us to expand and simplify expressions. By mastering this formula, you will become proficient in solving various mathematical problems and unlock a wide range of applications in mathematics and other fields.