(4m+1)^2

2 min read Jun 16, 2024
(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.

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