%5E2.jpeg "(4m+1)^2")
Expanding (4m + 1)²: A Step-by-Step Guide
The expression (4m + 1)² is a perfect square trinomial, meaning it's the result of squaring a binomial. To expand it, we can use the following steps:
Understanding the Concept
The expression (4m + 1)² is equivalent to multiplying (4m + 1) by itself:
(4m + 1)² = (4m + 1)(4m + 1)
Applying the FOIL Method
We can expand this expression using the FOIL method:
- First: Multiply the first terms of each binomial. (4m)(4m) = 16m²
- Outer: Multiply the outer terms of the binomials. (4m)(1) = 4m
- Inner: Multiply the inner terms of the binomials. (1)(4m) = 4m
- Last: Multiply the last terms of each binomial. (1)(1) = 1
Now, we combine the terms:
16m² + 4m + 4m + 1
Simplifying the Expression
Finally, we combine the like terms:
16m² + 8m + 1
Conclusion
Therefore, the expanded form of (4m + 1)² is 16m² + 8m + 1.
This process can be used to expand any perfect square trinomial. Remember to apply the FOIL method carefully to ensure accurate expansion.