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What is \((2x + 3)^2\)?

[tex]\[
(2x + 3)^2 = \square x^2 + \square x + \square
\][/tex]


Sagot :

Certainly! Let's expand the expression \((2x + 3)^2\) step-by-step.

First, recognize that \((2x + 3)^2\) means \((2x + 3) \cdot (2x + 3)\).

Using the distributive property (also known as the FOIL method for binomials), we expand this product:

1. First: Multiply the first terms of each binomial:
[tex]\[ 2x \cdot 2x = 4x^2 \][/tex]

2. Outer: Multiply the outer terms of the expression:
[tex]\[ 2x \cdot 3 = 6x \][/tex]

3. Inner: Multiply the inner terms of the expression:
[tex]\[ 3 \cdot 2x = 6x \][/tex]

4. Last: Multiply the last terms of each binomial:
[tex]\[ 3 \cdot 3 = 9 \][/tex]

Next, combine all these results together:

[tex]\[ 4x^2 + 6x + 6x + 9 \][/tex]

Combine the like terms \(6x + 6x\):

[tex]\[ 4x^2 + 12x + 9 \][/tex]

Therefore, the expanded form of \((2x + 3)^2\) is:

[tex]\[ 4x^2 + 12x + 9 \][/tex]

So, we can fill in the blanks as follows:

[tex]\[ (2x + 3)^2 = 4x^2 + 12x + 9 \][/tex]
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