Question

find the product.
$(3x - 2)^2$
options:

• $9x^2 - 6x + 4$
• $6x^2 + 4$
• $9x^2 + 4$
• $9x^2 - 12x + 4$

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = 3x\) and \(b = 2\).

Step2: Calculate each term

• For \(a^2\): \((3x)^2 = 9x^2\)
• For \(-2ab\): \(-2\times(3x)\times(2)= - 12x\)
• For \(b^2\): \(2^2 = 4\)

Step3: Combine the terms

Putting it all together, \((3x - 2)^2=9x^2-12x + 4\)

Answer:

\(9x^2 - 12x + 4\) (the option with this expression)