Answer :
To expand and simplify the expression \((m + 5)(m + 4)(m - 1)\), follow these steps:
### Step 1: Expand Two Factors First
First, we'll expand two of the factors: \((m + 5)(m + 4)\).
[tex]\[ (m + 5)(m + 4) = m(m+4) + 5(m+4) \][/tex]
Distribute \(m\) to each term inside the parentheses:
[tex]\[ m(m + 4) = m^2 + 4m \][/tex]
Distribute \(5\) to each term inside the parentheses:
[tex]\[ 5(m + 4) = 5m + 20 \][/tex]
Combine these results:
[tex]\[ m^2 + 4m + 5m + 20 = m^2 + 9m + 20 \][/tex]
### Step 2: Multiply the Result with the Third Factor
Now, take this result \((m^2 + 9m + 20)\) and multiply it by the third factor \((m - 1)\):
[tex]\[ (m^2 + 9m + 20)(m - 1) \][/tex]
Distribute each term in the first polynomial to each term in \( (m - 1) \):
[tex]\[ m^2(m - 1) + 9m(m - 1) + 20(m - 1) \][/tex]
Distribute each term individually:
[tex]\[ m^2 \cdot m = m^3 \][/tex]
[tex]\[ m^2 \cdot (-1) = -m^2 \][/tex]
[tex]\[ 9m \cdot m = 9m^2 \][/tex]
[tex]\[ 9m \cdot (-1) = -9m \][/tex]
[tex]\[ 20 \cdot m = 20m \][/tex]
[tex]\[ 20 \cdot (-1) = -20 \][/tex]
### Step 3: Combine Like Terms
Now, add all the terms together:
[tex]\[ m^3 - m^2 + 9m^2 - 9m + 20m - 20 \][/tex]
Combine the like terms:
[tex]\[ m^3 + (9m^2 - m^2) + (-9m + 20m) - 20 \][/tex]
This simplifies to:
[tex]\[ m^3 + 8m^2 + 11m - 20 \][/tex]
So, the expanded and simplified form of \((m + 5)(m + 4)(m - 1)\) is:
[tex]\[ \boxed{m^3 + 8m^2 + 11m - 20} \][/tex]
### Step 1: Expand Two Factors First
First, we'll expand two of the factors: \((m + 5)(m + 4)\).
[tex]\[ (m + 5)(m + 4) = m(m+4) + 5(m+4) \][/tex]
Distribute \(m\) to each term inside the parentheses:
[tex]\[ m(m + 4) = m^2 + 4m \][/tex]
Distribute \(5\) to each term inside the parentheses:
[tex]\[ 5(m + 4) = 5m + 20 \][/tex]
Combine these results:
[tex]\[ m^2 + 4m + 5m + 20 = m^2 + 9m + 20 \][/tex]
### Step 2: Multiply the Result with the Third Factor
Now, take this result \((m^2 + 9m + 20)\) and multiply it by the third factor \((m - 1)\):
[tex]\[ (m^2 + 9m + 20)(m - 1) \][/tex]
Distribute each term in the first polynomial to each term in \( (m - 1) \):
[tex]\[ m^2(m - 1) + 9m(m - 1) + 20(m - 1) \][/tex]
Distribute each term individually:
[tex]\[ m^2 \cdot m = m^3 \][/tex]
[tex]\[ m^2 \cdot (-1) = -m^2 \][/tex]
[tex]\[ 9m \cdot m = 9m^2 \][/tex]
[tex]\[ 9m \cdot (-1) = -9m \][/tex]
[tex]\[ 20 \cdot m = 20m \][/tex]
[tex]\[ 20 \cdot (-1) = -20 \][/tex]
### Step 3: Combine Like Terms
Now, add all the terms together:
[tex]\[ m^3 - m^2 + 9m^2 - 9m + 20m - 20 \][/tex]
Combine the like terms:
[tex]\[ m^3 + (9m^2 - m^2) + (-9m + 20m) - 20 \][/tex]
This simplifies to:
[tex]\[ m^3 + 8m^2 + 11m - 20 \][/tex]
So, the expanded and simplified form of \((m + 5)(m + 4)(m - 1)\) is:
[tex]\[ \boxed{m^3 + 8m^2 + 11m - 20} \][/tex]
