%5E2.jpeg "(2a+7)^2")
Expanding (2a + 7)^2
The expression (2a + 7)^2 represents the square of the binomial (2a + 7). To expand this, we need to understand the concept of squaring a binomial.
Understanding the Concept
Squaring a binomial means multiplying it by itself:
(2a + 7)^2 = (2a + 7) * (2a + 7)
Using the FOIL Method
The FOIL method is a common technique for expanding binomials:
- First: Multiply the first terms of each binomial.
- 2a * 2a = 4a^2
- Outer: Multiply the outer terms of the binomials.
- 2a * 7 = 14a
- Inner: Multiply the inner terms of the binomials.
- 7 * 2a = 14a
- Last: Multiply the last terms of each binomial.
- 7 * 7 = 49
Combining Like Terms
Now, we combine the results from each step:
4a^2 + 14a + 14a + 49
This simplifies to:
4a^2 + 28a + 49
Conclusion
Therefore, the expanded form of (2a + 7)^2 is 4a^2 + 28a + 49.