Answer :
Sure, let's simplify each of these expressions step-by-step.
### 1. Simplify \(-14cd - 2c^2d^2 + 15cd + 9c^2d^2 - 15cd\)
Combine like terms:
[tex]\[ (-14cd + 15cd - 15cd) + (-2c^2d^2 + 9c^2d^2) \][/tex]
Simplify each group of like terms:
[tex]\[ (-14 + 15 - 15)cd + (-2 + 9)c^2d^2 \][/tex]
[tex]\[ -14 + 15 - 15 = -14 + 0 = -14 \][/tex]
[tex]\[ -2 + 9 = 7 \][/tex]
So, we have:
[tex]\[ -14cd + 7c^2d^2 \][/tex]
We can factor out a common factor from these terms:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
Thus, the simplified form of the first expression is:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
### 2. Simplify \(7c^4d^4 - 14c^3d^3\)
Factor out the greatest common factor:
[tex]\[ 7c^3d^3(c \cdot d) - 7c^3d^3 \cdot 2 \][/tex]
[tex]\[ 7c^3d^3(c \cdot d - 2) \][/tex]
Thus, the simplified form of the second expression is:
[tex]\[ 7c^3d^3(c \cdot d - 2) \][/tex]
### 3. Simplify \(7c^2d^2 - 14cd\)
Factor out the greatest common factor:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
Thus, the simplified form of the third expression is:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
### 4. Simplify \(11c^2d^2 + 44cd\)
Factor out the greatest common factor:
[tex]\[ 11cd(c \cdot d + 4) \][/tex]
Thus, the simplified form of the fourth expression is:
[tex]\[ 11cd(c \cdot d + 4) \][/tex]
### 5. Simplify \(-7c^7d^7\)
This expression is already in its simplest form.
Thus, the simplified form of the fifth expression is:
[tex]\[ -7c^7d^7 \][/tex]
In summary, the simplified forms of the expressions are:
[tex]\[ 1) \quad 7cd(c \cdot d - 2) \][/tex]
[tex]\[ 2) \quad 7c^3d^3(c \cdot d - 2) \][/tex]
[tex]\[ 3) \quad 7cd(c \cdot d - 2) \][/tex]
[tex]\[ 4) \quad 11cd(c \cdot d + 4) \][/tex]
[tex]\[ 5) \quad -7c^7d^7 \][/tex]
### 1. Simplify \(-14cd - 2c^2d^2 + 15cd + 9c^2d^2 - 15cd\)
Combine like terms:
[tex]\[ (-14cd + 15cd - 15cd) + (-2c^2d^2 + 9c^2d^2) \][/tex]
Simplify each group of like terms:
[tex]\[ (-14 + 15 - 15)cd + (-2 + 9)c^2d^2 \][/tex]
[tex]\[ -14 + 15 - 15 = -14 + 0 = -14 \][/tex]
[tex]\[ -2 + 9 = 7 \][/tex]
So, we have:
[tex]\[ -14cd + 7c^2d^2 \][/tex]
We can factor out a common factor from these terms:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
Thus, the simplified form of the first expression is:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
### 2. Simplify \(7c^4d^4 - 14c^3d^3\)
Factor out the greatest common factor:
[tex]\[ 7c^3d^3(c \cdot d) - 7c^3d^3 \cdot 2 \][/tex]
[tex]\[ 7c^3d^3(c \cdot d - 2) \][/tex]
Thus, the simplified form of the second expression is:
[tex]\[ 7c^3d^3(c \cdot d - 2) \][/tex]
### 3. Simplify \(7c^2d^2 - 14cd\)
Factor out the greatest common factor:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
Thus, the simplified form of the third expression is:
[tex]\[ 7cd(c \cdot d - 2) \][/tex]
### 4. Simplify \(11c^2d^2 + 44cd\)
Factor out the greatest common factor:
[tex]\[ 11cd(c \cdot d + 4) \][/tex]
Thus, the simplified form of the fourth expression is:
[tex]\[ 11cd(c \cdot d + 4) \][/tex]
### 5. Simplify \(-7c^7d^7\)
This expression is already in its simplest form.
Thus, the simplified form of the fifth expression is:
[tex]\[ -7c^7d^7 \][/tex]
In summary, the simplified forms of the expressions are:
[tex]\[ 1) \quad 7cd(c \cdot d - 2) \][/tex]
[tex]\[ 2) \quad 7c^3d^3(c \cdot d - 2) \][/tex]
[tex]\[ 3) \quad 7cd(c \cdot d - 2) \][/tex]
[tex]\[ 4) \quad 11cd(c \cdot d + 4) \][/tex]
[tex]\[ 5) \quad -7c^7d^7 \][/tex]
