Questions: Find the following product. (9x-3)^2 (9x-3)^2=

Transcript text: Find the following product. \[ (9 x-3)^{2} \] \[ (9 x-3)^{2}= \]

Solution

Step 1: Expand the expression using the formula for squaring a binomial

The expression \((9x - 3)^2\) can be expanded using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = 9x\) and \(b = 3\).

Step 2: Apply the formula

Substitute \(a = 9x\) and \(b = 3\) into the formula: \[ (9x - 3)^2 = (9x)^2 - 2 \cdot (9x) \cdot 3 + 3^2 \]

Step 3: Simplify each term

Calculate each term separately: \[ (9x)^2 = 81x^2 \] \[ 2 \cdot (9x) \cdot 3 = 54x \] \[ 3^2 = 9 \]

Step 4: Combine the terms

Combine the simplified terms: \[ (9x - 3)^2 = 81x^2 - 54x + 9 \]

The final expanded form is: \[ (9x - 3)^2 = 81x^2 - 54x + 9 \]

\((9x - 3)^2 = \boxed{81x^2 - 54x + 9}\)

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