(x-3).jpeg "(x+6)(x-3)")
Expanding the Expression (x+6)(x-3)
The expression (x+6)(x-3) represents the product of two binomials. Expanding this expression involves multiplying each term in the first binomial by each term in the second binomial. This process is often referred to as FOIL (First, Outer, Inner, Last) method:
1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of the binomials: x * -3 = -3x
3. Inner: Multiply the inner terms of the binomials: 6 * x = 6x
4. Last: Multiply the last terms of each binomial: 6 * -3 = -18
Now, we combine the results of each step:
x² - 3x + 6x - 18
Finally, simplify by combining like terms:
x² + 3x - 18
Therefore, the expanded form of (x+6)(x-3) is x² + 3x - 18.
Applications of Expanding Binomials
Expanding binomials like (x+6)(x-3) has many applications in mathematics, including:
- Solving quadratic equations: By setting the expanded expression equal to zero, we can form a quadratic equation and solve for x.
- Factoring expressions: Recognizing that (x+6)(x-3) is the factored form of x² + 3x - 18 can be useful for simplifying expressions and solving equations.
- Graphing functions: The expanded form helps us understand the shape and behavior of the graph of the function represented by the expression.
- Algebraic manipulation: Expanding binomials is a fundamental step in many algebraic operations and manipulations.
Conclusion
Expanding the expression (x+6)(x-3) using the FOIL method is a straightforward process that results in the quadratic expression x² + 3x - 18. This expanded form has various applications in mathematics and helps us better understand the relationship between different algebraic expressions.