Sure! Let's solve the problem step-by-step:
We are given two expressions:
1. [tex]\( 3p(6q + p) \)[/tex]
2. [tex]\( 12p(3q - p) \)[/tex]
Our goal is to subtract the second expression from the first one.
Step 1: Write down the expressions
First expression:
[tex]\[ 3p(6q + p) \][/tex]
Second expression:
[tex]\[ 12p(3q - p) \][/tex]
Step 2: Distribute the terms
Let's expand both expressions:
First expression:
[tex]\[ 3p(6q + p) = 3p \cdot 6q + 3p \cdot p \][/tex]
[tex]\[ = 18pq + 3p^2 \][/tex]
Second expression:
[tex]\[ 12p(3q - p) = 12p \cdot 3q - 12p \cdot p \][/tex]
[tex]\[ = 36pq - 12p^2 \][/tex]
Step 3: Subtract the second expression from the first
Now subtract the expanded form of the second expression from the expanded form of the first expression:
[tex]\[ (18pq + 3p^2) - (36pq - 12p^2) \][/tex]
Step 4: Distribute the negative sign
[tex]\[ = 18pq + 3p^2 - 36pq + 12p^2 \][/tex]
Step 5: Combine like terms
Combine the terms with [tex]\(pq\)[/tex] and the terms with [tex]\(p^2\)[/tex]:
[tex]\[ pq: \quad 18pq - 36pq = -18pq \][/tex]
[tex]\[ p^2: \quad 3p^2 + 12p^2 = 15p^2 \][/tex]
Step 6: Write the final expression
Combining these results gives us:
[tex]\[ -18pq + 15p^2 \][/tex]
Or written another way, the result of subtracting [tex]\( 12p(3q - p) \)[/tex] from [tex]\( 3p(6q + p) \)[/tex] is:
[tex]\[ 15p^2 - 18pq \][/tex]
So, the final answer is:
[tex]\[ 15p^2 - 18pq \][/tex]
