(x+9)(x+9)

Jasonbradley

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Jun 17, 2024

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Expanding (x+9)(x+9)

The expression (x+9)(x+9) represents the product of two identical binomials. This is often called squaring a binomial. We can expand this expression using the distributive property or the FOIL method.

Using the Distributive Property

The distributive property states that a(b+c) = ab + ac. We can apply this twice to expand the expression:

1. Distribute the first term: (x+9)(x+9) = x(x+9) + 9(x+9)
2. Distribute again: x(x+9) + 9(x+9) = x² + 9x + 9x + 81

Finally, combine like terms:

x² + 9x + 9x + 81 = x² + 18x + 81

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. This mnemonic helps remember the steps for multiplying two binomials:

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of each binomial: x * 9 = 9x
3. Inner: Multiply the inner terms of each binomial: 9 * x = 9x
4. Last: Multiply the last terms of each binomial: 9 * 9 = 81

Add all the terms together: x² + 9x + 9x + 81 = x² + 18x + 81

Conclusion

Both the distributive property and the FOIL method lead to the same result: (x+9)(x+9) = x² + 18x + 81. This expanded form is a trinomial with a leading coefficient of 1 and a constant term of 81.