Let's simplify the given algebraic expression [tex]\( 5ab + 10ac - 2bd - Acd \)[/tex].
1. Identify the given values for constants and variables:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 1\)[/tex]
- [tex]\(c = 1\)[/tex]
- [tex]\(d = 1\)[/tex]
- [tex]\(A = 1\)[/tex]
2. Substitute these values into each term of the expression:
- For the term [tex]\(5ab\)[/tex]:
[tex]\[
5 \cdot a \cdot b = 5 \cdot 1 \cdot 1 = 5
\][/tex]
- For the term [tex]\(10ac\)[/tex]:
[tex]\[
10 \cdot a \cdot c = 10 \cdot 1 \cdot 1 = 10
\][/tex]
- For the term [tex]\(-2bd\)[/tex]:
[tex]\[
-2 \cdot b \cdot d = -2 \cdot 1 \cdot 1 = -2
\][/tex]
- For the term [tex]\(-Acd\)[/tex]:
[tex]\[
-A \cdot c \cdot d = -1 \cdot 1 \cdot 1 = -1
\][/tex]
3. Combine all the calculated terms:
[tex]\[
5 + 10 - 2 - 1
\][/tex]
4. Sum the terms to get the simplified expression:
[tex]\[
5 + 10 - 2 - 1 = 12
\][/tex]
Therefore, the simplified form of the expression [tex]\( 5ab + 10ac - 2bd - Acd \)[/tex] with the given values is:
[tex]\[
\boxed{12}
\][/tex]
Breaking down the results for clarity:
- The first term, [tex]\(5ab\)[/tex], evaluates to [tex]\(5\)[/tex].
- The second term, [tex]\(10ac\)[/tex], evaluates to [tex]\(10\)[/tex].
- The third term, [tex]\(-2bd\)[/tex], evaluates to [tex]\(-2\)[/tex].
- The fourth term, [tex]\(-Acd\)[/tex], evaluates to [tex]\(-1\)[/tex].
Summing these results gives us:
[tex]\[
5 + 10 - 2 - 1 = 12
\][/tex]
