Find the value of `3a + 2bc -3d^(3)`, given that a =5, b = 4, c = 3 and d = 2.

Answer

To find the value of the expression \(3a + 2bc - 3d^3\) given that \(a = 5\), \(b = 4\), \(c = 3\), and \(d = 2\), we will substitute the values of \(a\), \(b\), \(c\), and \(d\) into the expression step by step.

### Step 1: Substitute the values into the expression
The expression is:
\[ 3a + 2bc - 3d^3 \]
Substituting the values:
\[ 3(5) + 2(4)(3) - 3(2^3) \]

### Step 2: Calculate \(3a\)
Calculate \(3(5)\):
\[ 3(5) = 15 \]

### Step 3: Calculate \(2bc\)
Calculate \(2(4)(3)\):
\[ 2(4)(3) = 2 \times 4 = 8 \quad \text{and then} \quad 8 \times 3 = 24 \]

### Step 4: Calculate \(3d^3\)
Calculate \(d^3\) first:
\[ d^3 = 2^3 = 2 \times 2 \times 2 = 8 \]
Now calculate \(3(8)\):
\[ 3(8) = 24 \]

### Step 5: Combine all parts of the expression
Now we can substitute back into the expression:
\[ 15 + 24 - 24 \]

### Step 6: Simplify the expression
Now simplify:
\[ 15 + 24 = 39 \]
Then,
\[ 39 - 24 = 15 \]

### Final Answer
Thus, the value of the expression \(3a + 2bc - 3d^3\) is:
\[ \boxed{15} \]