(5a+2)^2

Jasonbradley

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Jun 16, 2024

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Expanding (5a + 2)^2

The expression (5a + 2)^2 represents the square of the binomial (5a + 2). To expand this expression, we can use the FOIL method or the square of a binomial formula.

Expanding using FOIL method:

FOIL stands for First, Outer, Inner, Last. This method helps us multiply two binomials.

1. First: Multiply the first terms of each binomial: (5a) * (5a) = 25a^2
2. Outer: Multiply the outer terms of the binomials: (5a) * (2) = 10a
3. Inner: Multiply the inner terms of the binomials: (2) * (5a) = 10a
4. Last: Multiply the last terms of the binomials: (2) * (2) = 4

Now, add all the results together:

25a^2 + 10a + 10a + 4 = 25a^2 + 20a + 4

Expanding using Square of a Binomial Formula:

The formula for the square of a binomial is: (a + b)^2 = a^2 + 2ab + b^2

In our case, a = 5a and b = 2. Applying the formula:

(5a + 2)^2 = (5a)^2 + 2(5a)(2) + (2)^2

Simplifying:

(5a + 2)^2 = 25a^2 + 20a + 4

Conclusion:

We can see that both methods lead to the same result: (5a + 2)^2 = 25a^2 + 20a + 4.

Remember, choosing which method to use depends on your personal preference and comfort level. Both methods are valid and effective for expanding the square of a binomial.