Final answer:
To make the expression u² + 18u + prod a perfect square, we need to find the value of 'prod' that will make it a perfect square.
Step-by-step explanation:
To make the expression u² + 18u + prod a perfect square, we need to find the value of 'prod' that will make it a perfect square. In order for an algebraic expression to be a perfect square, the coefficient of the middle term must be equal to twice the square root of the product of the first and last term. In this case, the coefficient of the middle term is 18, so we need to find a number that satisfies this condition. Let's set up the equation:
18 = 2√(u² × prod)
Solving for 'prod', we can square both sides:
18² = 4u² × prod
324 = 4u² × prod
Now we can divide both sides by 4u²:
prod = 324 / (4u²)