Expand and simplify (3x-2) squared

Expand and simplify (3x-2) squared

The Correct Answer and Explanation is:

To expand and simplify the expression ((3x – 2)^2), we can follow these steps:

Step 1: Understand the square of a binomial

The expression ((3x – 2)^2) is a binomial raised to the second power. When you square a binomial, you use the square of a binomial formula:

[
(a – b)^2 = a^2 – 2ab + b^2
]

In this case, (a = 3x) and (b = 2), so we can apply this formula to expand the expression.

Step 2: Apply the formula to expand

Now, let’s use the formula to expand ((3x – 2)^2):

[
(3x – 2)^2 = (3x)^2 – 2(3x)(2) + (2)^2
]

Step 3: Simplify each term

1. Square the first term: ((3x)^2 = 9x^2)
2. Multiply the middle term: (-2(3x)(2) = -12x)
3. Square the last term: ((2)^2 = 4)

Step 4: Combine the terms

Now, we put all the simplified terms together:

[
(3x – 2)^2 = 9x^2 – 12x + 4
]

Final Answer:

The expanded and simplified form of ((3x – 2)^2) is:

[
9x^2 – 12x + 4
]

Explanation:

Expanding and simplifying ((3x – 2)^2) requires recognizing that this is a binomial squared. The formula ((a – b)^2 = a^2 – 2ab + b^2) is applied by first squaring the first term, multiplying the first and second terms, and then squaring the second term. After performing these operations, we combine the terms to get the final expression (9x^2 – 12x + 4). This process is essential in algebra as it helps in simplifying expressions and solving equations efficiently.