(x+8)^2

Jasonbradley

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Jun 17, 2024

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Expanding (x+8)^2

The expression (x+8)^2 represents the square of the binomial (x+8). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Expanding using FOIL

FOIL stands for First, Outer, Inner, Last. This method involves multiplying each term in the first binomial by each term in the second binomial.

1. First: Multiply the first terms of each binomial: x * x = x^2
2. Outer: Multiply the outer terms of the binomials: x * 8 = 8x
3. Inner: Multiply the inner terms of the binomials: 8 * x = 8x
4. Last: Multiply the last terms of each binomial: 8 * 8 = 64

Adding all the terms together, we get:

x^2 + 8x + 8x + 64

Combining the like terms, we get the final expanded form:

(x+8)^2 = x^2 + 16x + 64

Expanding using the Square of a Binomial Formula

The square of a binomial formula states:

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

In this case, a = x and b = 8. Applying the formula:

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

Simplifying the expression:

(x + 8)^2 = x^2 + 16x + 64

Conclusion

Both methods, FOIL and the square of a binomial formula, lead to the same expanded form of (x+8)^2: x^2 + 16x + 64. This expression is a trinomial with a degree of 2. It represents a parabola when graphed.