Certainly! Let's simplify the given algebraic expression step by step:
Expression:
[tex]\[ 2b(3a - c) + 12ac - b^2 \][/tex]
### Step 1: Distribute \(2b\) in the first term
Distribute \(2b\) across the parentheses in the term \(2b(3a - c)\):
[tex]\[ 2b(3a - c) = 2b \cdot 3a - 2b \cdot c \][/tex]
[tex]\[ = 6ab - 2bc \][/tex]
### Step 2: Substitute the expanded term back into the expression
Now, replace \(2b(3a - c)\) in the original expression with its expanded form \(6ab - 2bc\):
[tex]\[ 6ab - 2bc + 12ac - b^2 \][/tex]
### Step 3: Look for like terms
In the current expression
[tex]\[ 6ab - 2bc + 12ac - b^2 \][/tex]
there are no like terms to combine as each term is unique:
- \(6ab\): A term involving both \(a\) and \(b\).
- \(-2bc\): A term involving both \(b\) and \(c\).
- \(12ac\): A term involving both \(a\) and \(c\).
- \(-b^2\): A squared term in \(b\).
### Final Simplified Expression
Since there are no like terms to combine further, the simplified expression is:
[tex]\[ 6ab - 2bc + 12ac - b^2 \][/tex]
So, the final answer is:
[tex]\[ 6ab - 2bc + 12ac - b^2 \][/tex]
