(4m+3)(m^2-4m+4)-(2m-3)(2m^2+3m-4)

Jasonbradley

2 min read

·

Jun 16, 2024

34

Share

Simplifying the Expression: (4m+3)(m^2-4m+4)-(2m-3)(2m^2+3m-4)

This expression involves multiplying two binomials and then subtracting the product of two other binomials. We can simplify it by following the steps below:

1. Expanding the products

• First product: (4m+3)(m^2-4m+4)
  • We can use the FOIL (First, Outer, Inner, Last) method to expand this:
    • First: 4m * m^2 = 4m^3
    • Outer: 4m * -4m = -16m^2
    • Inner: 3 * m^2 = 3m^2
    • Last: 3 * -4m = -12m
    • Last: 3 * 4 = 12
  • Combining like terms, we get: 4m^3 - 13m^2 - 12m + 12
• Second product: (2m-3)(2m^2+3m-4)
  • Using FOIL again:
    • First: 2m * 2m^2 = 4m^3
    • Outer: 2m * 3m = 6m^2
    • Inner: -3 * 2m^2 = -6m^2
    • Last: -3 * 3m = -9m
    • Last: -3 * -4 = 12
  • Combining like terms: 4m^3 + 12m - 9m + 12

2. Subtracting the products

Now we subtract the second product from the first product:

(4m^3 - 13m^2 - 12m + 12) - (4m^3 + 12m - 9m + 12)

3. Simplifying the result

• Since we are subtracting, we change the signs of the terms inside the second parentheses: 4m^3 - 13m^2 - 12m + 12 - 4m^3 - 12m + 9m - 12
• Combining like terms: -13m^2 - 15m

Therefore, the simplified form of the given expression is -13m^2 - 15m.