What expression is equivalent to the product of m and n if m = x^2 + 3 and n = 5x + 9?

To determine the expression that is equivalent to the product of m and n, let’s first substitute the given expressions:

We have:

• m = x² + 3
• n = 5x + 9

Now, we need to multiply m and n:

mn = (x2 + 3)(5x + 9)

To perform the multiplication, we will use the distributive property:

mn = x2 * 5x + x2 * 9 + 3 * 5x + 3 * 9

Now, simplifying each term gives:

• x2 * 5x = 5x3
• x2 * 9 = 9x2
• 3 * 5x = 15x
• 3 * 9 = 27

Putting it all together, we get:

mn = 5x3 + 9x2 + 15x + 27

Therefore, the expression equivalent to mn is:

5x³ + 9x² + 15x + 27