(x%2B3).jpeg "(x+6)(x+3)")
Expanding the Expression (x+6)(x+3)
This expression represents the product of two binomials: (x+6) and (x+3). To expand this expression, we can use the FOIL method:
First: Multiply the first terms of each binomial.
- x * x = x²
Outer: Multiply the outer terms of the binomials.
- x * 3 = 3x
Inner: Multiply the inner terms of the binomials.
- 6 * x = 6x
Last: Multiply the last terms of each binomial.
- 6 * 3 = 18
Now, combine all the terms:
x² + 3x + 6x + 18
Finally, simplify by combining like terms:
x² + 9x + 18
Therefore, the expanded form of (x+6)(x+3) is x² + 9x + 18.
Understanding the FOIL Method
The FOIL method is a mnemonic device to help remember the steps in expanding the product of two binomials. It stands for:
- First
- Outer
- Inner
- Last
By following this order, you ensure that all possible combinations of terms are multiplied and none are missed.
Applications of Expanding Binomials
Expanding binomials is a fundamental skill in algebra with numerous applications, including:
- Solving quadratic equations: By factoring a quadratic equation into two binomials, you can find its solutions.
- Graphing quadratic functions: The expanded form of a quadratic function helps you determine its vertex, intercepts, and shape.
- Simplifying expressions: Expanding binomials can simplify complex algebraic expressions.
Understanding how to expand binomials is crucial for mastering more advanced concepts in algebra and other mathematical disciplines.