(2x+5)^2 Expand

Jasonbradley

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Jun 16, 2024

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Expanding (2x + 5)^2

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

Using the FOIL Method

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

Now, combine the results and simplify: 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25

Using the Square of a Binomial Formula

The square of a binomial formula states that (a + b)^2 = a^2 + 2ab + b^2. We can apply this formula to our expression:

1. Identify a and b: In our case, a = 2x and b = 5.
2. Substitute into the formula: (2x)^2 + 2(2x)(5) + (5)^2
3. Simplify: 4x^2 + 20x + 25

Therefore, expanding (2x + 5)^2 using either method results in the same answer: 4x^2 + 20x + 25.