Sure! Let's solve the given expression step-by-step. The given expression is:
[tex]\[ Pqr - 6Pqr + 7q^2 - 4P^2 \][/tex]
We will substitute the values [tex]\( P = 1 \)[/tex], [tex]\( q = 4 \)[/tex], and [tex]\( r = 2 \)[/tex] into the expression and simplify step-by-step:
1. First Term: [tex]\( Pqr \)[/tex]
[tex]\[
Pqr = 1 \cdot 4 \cdot 2 = 8
\][/tex]
2. Second Term: [tex]\( -6Pqr \)[/tex]
[tex]\[
-6Pqr = -6 \cdot 1 \cdot 4 \cdot 2 = -48
\][/tex]
3. Third Term: [tex]\( 7q^2 \)[/tex]
[tex]\[
7q^2 = 7 \cdot (4)^2 = 7 \cdot 16 = 112
\][/tex]
4. Fourth Term: [tex]\( -4P^2 \)[/tex]
[tex]\[
-4P^2 = -4 \cdot (1)^2 = -4
\][/tex]
Now, let's combine all the calculated terms:
[tex]\[
Pqr - 6Pqr + 7q^2 - 4P^2 = 8 - 48 + 112 - 4
\][/tex]
Finally, we add and subtract these values together:
[tex]\[
8 - 48 + 112 - 4 = 68
\][/tex]
So, the simplified result of the given expression is [tex]\( 68 \)[/tex].
To summarize the individual term calculations and the final result step-by-step:
- First term [tex]\( Pqr = 8 \)[/tex]
- Second term [tex]\( -6Pqr = -48 \)[/tex]
- Third term [tex]\( 7q^2 = 112 \)[/tex]
- Fourth term [tex]\( -4P^2 = -4 \)[/tex]
And the overall result is [tex]\( 68 \)[/tex].
