Question

expand and simplify ((4x - 3)^2)
options:

• (some unreadable option)
• (16x^2 + 24x + 9)
• (16x^2 - 24x + 9)
• (16x^2 + 9)
• (16x^2 - 9)
• (16x^2 - 12x + 9)
• (16x^2 + 12x + 9)

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = 4x\) and \(b = 3\).

Step2: Apply the formula

First, calculate \(a^2=(4x)^2 = 16x^2\). Then, calculate \(2ab = 2\times(4x)\times3=24x\). And \(b^2 = 3^2 = 9\).
Now, substitute these into the formula: \((4x - 3)^2=(4x)^2-2\times(4x)\times3 + 3^2\)

Step3: Simplify the expression

Simplify each term: \((4x)^2 = 16x^2\), \(-2\times(4x)\times3=-24x\), and \(3^2 = 9\). So the expanded form is \(16x^2-24x + 9\).

Answer:

\(16x^2 - 24x + 9\) (corresponding to the option with this expression)