(4x+1)^2 Simplified

Jasonbradley

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Jun 16, 2024

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Simplifying (4x+1)^2

The expression (4x+1)^2 represents the square of the binomial (4x+1). To simplify this expression, we can use the FOIL method or the square of a binomial formula.

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply two binomials by multiplying each term of the first binomial with each term of the second binomial.

1. First: Multiply the first terms of both binomials: (4x) * (4x) = 16x²
2. Outer: Multiply the outer terms of the binomials: (4x) * (1) = 4x
3. Inner: Multiply the inner terms of the binomials: (1) * (4x) = 4x
4. Last: Multiply the last terms of both binomials: (1) * (1) = 1

Now, combine the terms: 16x² + 4x + 4x + 1

Finally, simplify by combining the like terms: 16x² + 8x + 1

Using the Square of a Binomial Formula

The square of a binomial formula states: (a + b)² = a² + 2ab + b²

In this case, a = 4x and b = 1. Substituting these values into the formula:

(4x + 1)² = (4x)² + 2(4x)(1) + (1)²

Simplifying the expression:

(4x + 1)² = 16x² + 8x + 1

Conclusion

Therefore, the simplified form of (4x+1)² is 16x² + 8x + 1. Both the FOIL method and the square of a binomial formula yield the same result. You can choose whichever method you find easier to apply.