Question

perfect square trinomial:
$(a - b)^2 = (a - b)(a - b) = a^2 - 2ab + b^2$
find the product of $(k - 9)^2$ using the perfect square trinomial rule shown on the left.
the product $(k - 9)^2$ can also be written as
the product is $k^2 - \square k + \square$.

Explanation:

Step1: Match to perfect square form

Identify $a=k$, $b=9$ for $(a-b)^2$.

Step2: Expand using the rule

Substitute into $a^2 - 2ab + b^2$:

$$\begin{align*} (k-9)^2 &= k^2 - 2(k)(9) + 9^2 \\ &= k^2 - 18k + 81 \end{align*}$$

Step3: Rewrite the squared term

$(k-9)^2$ is equivalent to $(k-9)(k-9)$.

Answer:

The product $(k - 9)^2$ can also be written as $\boldsymbol{(k-9)(k-9)}$.
The product is $\boldsymbol{k^2 - 18k + 81}$.