2(ab+bc+ca) Formula: A Powerful Tool in Algebra
In algebra, the 2(ab+bc+ca) formula is a widely used and powerful tool for simplifying complex expressions and solving equations. This formula is commonly used in various mathematical disciplines, including algebra, geometry, and trigonometry.
What is the 2(ab+bc+ca) Formula?
The 2(ab+bc+ca) formula is a mathematical expression that represents the sum of the products of three variables a, b, and c, taken two at a time. Mathematically, it can be written as:
2(ab + bc + ca)
This formula is often used to simplify complex expressions involving the variables a, b, and c.
How to Apply the 2(ab+bc+ca) Formula?
To apply the 2(ab+bc+ca) formula, follow these steps:
- Identify the variables
a,b, andcin the given expression. - Write down the formula:
2(ab + bc + ca). - Plug in the values of
a,b, andcinto the formula. - Simplify the expression by evaluating the products and sums.
Examples of Using the 2(ab+bc+ca) Formula
Here are a few examples to illustrate the application of the 2(ab+bc+ca) formula:
Example 1:
Simplify the expression 2xy + 2yz + 2zx, where x = 2, y = 3, and z = 4.
Solution:
Using the 2(ab+bc+ca) formula, we get:
2(ab + bc + ca) = 2(2*3 + 3*4 + 4*2)
= 2(6 + 12 + 8)
= 2(26)
= 52
Example 2:
Solve the equation x^2 + y^2 + z^2 - 2(xy + yz + zx) = 0, where x = 1, y = 2, and z = 3.
Solution:
Rearranging the equation, we get:
x^2 + y^2 + z^2 = 2(xy + yz + zx)
Using the 2(ab+bc+ca) formula, we get:
1^2 + 2^2 + 3^2 = 2(1*2 + 2*3 + 3*1)
= 1 + 4 + 9 = 2(2 + 6 + 3)
= 14 = 2(11)
= 22
Thus, the equation is satisfied.
Conclusion
The 2(ab+bc+ca) formula is a powerful tool in algebra that can be used to simplify complex expressions and solve equations. By applying this formula, you can easily evaluate and simplify expressions involving the variables a, b, and c. With practice and patience, you can master this formula and become proficient in solving algebraic equations.
