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Simplify: [tex]-14cd - 2c^2d^2 + 15cd + 9c^2d^2 - 15cd[/tex]

A. [tex]7c^4d^4 - 14c^3d^3[/tex]
B. [tex]7c^2d^2 - 14cd[/tex]
C. [tex]11c^2d^2 + 44cd[/tex]
D. [tex]-7c^7d^7[/tex]



Answer :

GinnyAnswer
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.

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