Q. \((x-3)^2\)

We are asked to expand the expression \( (x-3)^2 \). To do this step by step, we will use the algebra formula for squaring a binomial.

Step 1: Identify the binomial parts

The expression is \( (x-3)^2 \). This is a binomial of the form \( (a-b)^2 \), where:

• \(a = x\)
• \(b = 3\)

Step 2: Use the binomial square formula

The formula for squaring a binomial \( (a-b)^2 \) is:

\[
(a-b)^2 = a^2 – 2ab + b^2
\]

Step 3: Substitute \(a=x\) and \(b=3\)

Substitute into the formula:

\[
(x-3)^2 = x^2 – 2(x)(3) + 3^2
\]

Step 4: Simplify each term

Now simplify term by term.

Term 1:

\[
x^2
\]

Term 2:

Compute \( -2(x)(3) \):

\[
-2(x)(3) = -6x
\]

Term 3:

Compute \( 3^2 \):

\[
3^2 = 9
\]

Step 5: Combine the simplified terms

Put everything together:

\[
(x-3)^2 = x^2 – 6x + 9
\]

Final Answer

\[
(x-3)^2 = x^2 – 6x + 9
\]