Question

finding a perfect square trinomial

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
dropdown menu options: \\((k-9)(k+9)\\), \\((k-9)(k-9)\\), \\((k+9)(k+9)\\)
\\(k^2 - \quadk + \quad\\)

Explanation:

Identify the factored form of the squared binomial

$$ (k-9)^2 = (k-9)(k-9) $$

Apply the perfect square trinomial formula

Using \((a-b)^2 = a^2 - 2ab + b^2\) with \(a = k\) and \(b = 9\):

$$ (k-9)^2 = k^2 - 2(k)(9) + 9^2 $$

Simplify the terms

$$ (k-9)^2 = k^2 - 18k + 81 $$

Answer:

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 <blank>\((k-9)(k-9)\)</blank> \(=\) \(k^2 -\) <blank>\(18\)</blank> \(k +\) <blank>\(81\)</blank>