Sure, let's find the product of [tex]\((k-9)^2\)[/tex] using the perfect square trinomial rule.
The perfect square trinomial rule states:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
Here, we have [tex]\(a = k\)[/tex] and [tex]\(b = 9\)[/tex]. Let's substitute [tex]\(k\)[/tex] and [tex]\(9\)[/tex] into the formula.
1. Square the first term [tex]\(a\)[/tex]:
[tex]\[
a^2 = k^2
\][/tex]
2. Subtract twice the product of the first and second term:
[tex]\[
-2ab = -2 \cdot k \cdot 9 = -18k
\][/tex]
3. Add the square of the second term [tex]\(b\)[/tex]:
[tex]\[
b^2 = 9^2 = 81
\][/tex]
Putting it all together, we get:
[tex]\[
(k - 9)^2 = k^2 - 18k + 81
\][/tex]
Thus, to fill in the blanks in the given product:
- The expanded form of [tex]\((k-9)^2\)[/tex] is [tex]\(k^2 - 18k + 81\)[/tex].
So, the final answers are:
- The product [tex]\((k-9)^2\)[/tex] can also be written as [tex]\(k^2 - 18k + 81\)[/tex].
- The product is [tex]\(k^2 -\ 18k +\ 81\)[/tex].
