%5E2-5.jpeg "(x+3)^2-5")
Expanding and Simplifying (x+3)^2 - 5
This expression combines several mathematical concepts, including:
- Squaring a binomial: We need to understand how to expand (x+3)^2
- Order of operations: We need to perform the operations in the correct order.
Let's break it down step-by-step:
Expanding (x+3)^2
Remember that squaring a binomial means multiplying it by itself:
(x + 3)^2 = (x + 3)(x + 3)
To expand this, we can use the FOIL method (First, Outer, Inner, Last):
- First: x * x = x^2
- Outer: x * 3 = 3x
- Inner: 3 * x = 3x
- Last: 3 * 3 = 9
Combining the terms:
(x + 3)^2 = x^2 + 3x + 3x + 9 = x^2 + 6x + 9
Simplifying the Entire Expression
Now we can substitute this back into our original expression:
(x + 3)^2 - 5 = x^2 + 6x + 9 - 5
Finally, combine the constant terms:
x^2 + 6x + 4
Conclusion
The simplified form of (x+3)^2 - 5 is x^2 + 6x + 4. This process involved expanding a binomial, applying the order of operations, and combining like terms.