If m = x^2 + 3 and n = x + 5x + 9, which expression is equivalent to mn = x?

To find the expression equivalent to mn, we first need to simplify m and n based on the given equations.

Starting with m:

m = x² + 3

Next, let’s simplify n:

n = x + 5x + 9 = 6x + 9

Now, we can find the product mn:

mn = (x² + 3)(6x + 9)

To simplify this, we apply the distributive property (also known as the FOIL method for binomials):

• First, multiply each term in the first expression by each term in the second expression:
• m * n = (x² * 6x) + (x² * 9) + (3 * 6x) + (3 * 9)

This gives us:

• 6x³ + 9x² + 18x + 27

So, the expression equivalent to mn is:

6x³ + 9x² + 18x + 27

This is the expanded form of the product of m and n, which we can use to analyze further or use in different equations as needed.