(x+4)^2 Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying (x + 4)^2

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

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials together. Here's how it works:

1. First: Multiply the first terms of each binomial: x * x = x^2
2. Outer: Multiply the outer terms of the binomials: x * 4 = 4x
3. Inner: Multiply the inner terms of the binomials: 4 * x = 4x
4. Last: Multiply the last terms of each binomial: 4 * 4 = 16

Now, we add all the terms together: x^2 + 4x + 4x + 16

Combining like terms, we get:

(x + 4)^2 = x^2 + 8x + 16

Using the Square of a Binomial Pattern

The square of a binomial pattern states:

(a + b)^2 = a^2 + 2ab + b^2

In our case, a = x and b = 4. Substituting these values into the pattern, we get:

(x + 4)^2 = x^2 + 2(x)(4) + 4^2

Simplifying, we get:

(x + 4)^2 = x^2 + 8x + 16

Conclusion

Therefore, both the FOIL method and the square of a binomial pattern lead to the simplified expression: (x + 4)^2 = x^2 + 8x + 16. Remember, understanding these methods helps you simplify similar expressions and solve equations efficiently.