Certainly! Let’s simplify each of the given expressions step-by-step.
### Expression 1: \(-14 c d-2 c^2 d^2+15 c d+9 c^2 d^2-15 c d\)
1. Combine like terms:
[tex]\[
-14 c d + 15 c d - 15 c d = -14 c d
\][/tex]
[tex]\[
-2 c^2 d^2 + 9 c^2 d^2 = 7 c^2 d^2
\][/tex]
2. Put them together:
[tex]\[
-14 c d + 7 c^2 d^2
\][/tex]
3. Factor out the common factor \((c d)\):
[tex]\[
-14 c d + 7 c^2 d^2 = 7 c d (c d - 2)
\][/tex]
### Expression 2: \(7 c^4 d^4-14 c^3 d^3\)
1. Factor out the common factor \(7 c^3 d^3\):
[tex]\[
7 c^4 d^4 - 14 c^3 d^3 = 7 c^3 d^3 (c d - 2)
\][/tex]
### Expression 3: \(7 c^2 d^2-14 c d\)
1. Factor out the common factor \(7 c d\):
[tex]\[
7 c^2 d^2 - 14 c d = 7 c d (c d - 2)
\][/tex]
### Expression 4: \(11 c^2 d^2+44 c d\)
1. Factor out the common factor \(11 c d\):
[tex]\[
11 c^2 d^2 + 44 c d = 11 c d (c d + 4)
\][/tex]
### Expression 5: \(-7 c^7 d^7\)
1. The expression is already in its simplest form. Nothing to factor out or simplify further.
So, the simplified expressions are:
1. \(7 c d (c d - 2)\)
2. \(7 c^3 d^3 (c d - 2)\)
3. \(7 c d (c d - 2)\)
4. \(11 c d (c d + 4)\)
5. \(-7 c^7 d^7\)
And these match perfectly with the given results.
