Final answer:
To find the product of (k – 9)^2 using the perfect square trinomial rule, we need to recognize that this expression is in the form of a perfect square trinomial.
The perfect square trinomial rule states that the square of a binomial is equal to the square of the first term, plus double the product of the first term and the second term, plus the square of the second term. So, the product of (k – 9)^2 is k^2 - 18k + 81.
Step-by-step explanation:
An expression is said to be a perfect square trinomial if it is of the form ax2+bx+c and b2 = 4ac is satisfied. For example, comparing the expression x2 + 2x + 1, to the forms mentioned above, we find that a = 1, b = 2 and c = 1, therefore, b2 = 4 and 4 × a × c = 4 × 1 × 1, which is 4.
To find the product of (k – 9)^2 using the perfect square trinomial rule, we need to recognize that this expression is in the form of a perfect square trinomial. The perfect square trinomial rule states that the square of a binomial is equal to the square of the first term, plus double the product of the first term and the second term, plus the square of the second term.
So, applying this rule to (k – 9)^2:
(k – 9)^2 = k^2 + 2(k)(-9) + (-9)^2
Simplifying this expression, we get:
(k – 9)^2 = k^2 - 18k + 81