%5E2.jpeg "(4+7a^2)^2")
Expanding (4 + 7a^2)^2
The expression (4 + 7a^2)^2 represents the square of a binomial. To expand it, we can use the FOIL method or the square of a binomial pattern.
Expanding using FOIL
FOIL stands for First, Outer, Inner, Last, and it's a way to remember how to multiply two binomials.
- First: Multiply the first terms of each binomial: 4 * 4 = 16
- Outer: Multiply the outer terms of the binomials: 4 * 7a^2 = 28a^2
- Inner: Multiply the inner terms of the binomials: 7a^2 * 4 = 28a^2
- Last: Multiply the last terms of each binomial: 7a^2 * 7a^2 = 49a^4
Now, add all the results: 16 + 28a^2 + 28a^2 + 49a^4
Combining like terms, we get: 49a^4 + 56a^2 + 16
Expanding using the Square of a Binomial Pattern
The square of a binomial pattern is (a + b)^2 = a^2 + 2ab + b^2.
Applying this to our expression:
- a = 4
- b = 7a^2
Substituting: (4 + 7a^2)^2 = 4^2 + 2 * 4 * 7a^2 + (7a^2)^2
Simplifying: 49a^4 + 56a^2 + 16
Conclusion
Therefore, the expanded form of (4 + 7a^2)^2 is 49a^4 + 56a^2 + 16. Both the FOIL method and the square of a binomial pattern lead to the same result. Choose the method that you find easier to apply.