Questions: Use the distributive property to find the product. (4 m-5 y)(2 m+3 y) (4 m-5 y)(2 m+3 y) = (Simplify your answer.)

Solution Steps

To solve the given problem using the distributive property, we need to apply the FOIL (First, Outer, Inner, Last) method to expand the expression. This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

To find the product of the expression \((4m - 5y)(2m + 3y)\), we apply the distributive property, which involves multiplying each term in the first binomial by each term in the second binomial.

Using the FOIL method:

• First: \(4m \cdot 2m = 8m^2\)
• Outer: \(4m \cdot 3y = 12my\)
• Inner: \(-5y \cdot 2m = -10my\)
• Last: \(-5y \cdot 3y = -15y^2\)

Combining these results gives: \[ 8m^2 + 12my - 10my - 15y^2 \]

Now, we combine the like terms \(12my\) and \(-10my\): \[ 8m^2 + (12my - 10my) - 15y^2 = 8m^2 + 2my - 15y^2 \]

Final Answer