%5E2.jpeg "(4a+7)^2")
Expanding (4a + 7)^2
The expression (4a + 7)^2 represents the square of a binomial. To expand this, we can use the following methods:
1. Using the FOIL Method
The FOIL method stands for First, Outer, Inner, Last. This method is used to multiply two binomials.
- First: Multiply the first terms of each binomial: 4a * 4a = 16a²
- Outer: Multiply the outer terms of the binomials: 4a * 7 = 28a
- Inner: Multiply the inner terms of the binomials: 7 * 4a = 28a
- Last: Multiply the last terms of each binomial: 7 * 7 = 49
Now, add all the terms together:
16a² + 28a + 28a + 49 = 16a² + 56a + 49
2. Using the Square of a Binomial Formula
The formula for squaring a binomial is:
(a + b)² = a² + 2ab + b²
In this case, a = 4a and b = 7. Substitute these values into the formula:
(4a + 7)² = (4a)² + 2(4a)(7) + (7)²
Simplify the expression:
(4a + 7)² = 16a² + 56a + 49
Conclusion
Both methods lead to the same expanded form of (4a + 7)², which is 16a² + 56a + 49. This is a trinomial, meaning it has three terms. Remember that the FOIL method is a specific application of the distributive property, while the square of a binomial formula offers a more general approach.