(a+3b)^2

Jasonbradley

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Jun 16, 2024

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Expanding (a + 3b)^2

The expression (a + 3b)^2 represents the square of the binomial (a + 3b). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Using FOIL Method

FOIL stands for First, Outer, Inner, Last. It helps us multiply two binomials:

1. First: Multiply the first terms of each binomial: a * a = a^2
2. Outer: Multiply the outer terms of the binomials: a * 3b = 3ab
3. Inner: Multiply the inner terms of the binomials: 3b * a = 3ab
4. Last: Multiply the last terms of each binomial: 3b * 3b = 9b^2

Now, add all the terms together:

a^2 + 3ab + 3ab + 9b^2

Finally, combine the like terms:

a^2 + 6ab + 9b^2

Using Square of a Binomial Formula

The square of a binomial formula states:

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

In our case, a = a and b = 3b. Substituting these values into the formula:

(a + 3b)^2 = a^2 + 2(a)(3b) + (3b)^2

Simplifying:

a^2 + 6ab + 9b^2

Conclusion

Both methods lead to the same answer: (a + 3b)^2 = a^2 + 6ab + 9b^2. Understanding these methods allows you to expand similar expressions easily and efficiently.