Factoring Common Monomial Factor - YouTube - Free Printable

Problem: Factoring Common Monomial Factor

The task is to factor each expression by identifying and extracting the greatest common monomial factor. The general form of factoring a common monomial factor is:

$$
ab + ac = a(b + c)
$$

We will apply this principle to each of the given expressions.

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1. \( 4b + 4c \)

- Step 1: Identify the common factor in both terms.
- The terms are \( 4b \) and \( 4c \).
- The greatest common factor (GCF) of \( 4b \) and \( 4c \) is \( 4 \).

- Step 2: Factor out the GCF.
- Write \( 4b + 4c \) as \( 4(b + c) \).

- Final Answer:
$$
4b + 4c = 4(b + c)
$$

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2. \( 5m - 5n \)

- Step 1: Identify the common factor in both terms.
- The terms are \( 5m \) and \( -5n \).
- The greatest common factor (GCF) of \( 5m \) and \( -5n \) is \( 5 \).

- Step 2: Factor out the GCF.
- Write \( 5m - 5n \) as \( 5(m - n) \).

- Final Answer:
$$
5m - 5n = 5(m - n)
$$

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3. \( 12b + 6c \)

- Step 1: Identify the common factor in both terms.
- The terms are \( 12b \) and \( 6c \).
- The greatest common factor (GCF) of \( 12b \) and \( 6c \) is \( 6 \).

- Step 2: Factor out the GCF.
- Write \( 12b + 6c \) as \( 6(2b + c) \).

- Final Answer:
$$
12b + 6c = 6(2b + c)
$$

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4. \( 15m - 9n \)

- Step 1: Identify the common factor in both terms.
- The terms are \( 15m \) and \( -9n \).
- The greatest common factor (GCF) of \( 15m \) and \( -9n \) is \( 3 \).

- Step 2: Factor out the GCF.
- Write \( 15m - 9n \) as \( 3(5m - 3n) \).

- Final Answer:
$$
15m - 9n = 3(5m - 3n)
$$

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5. \( b^3 + b^2 \)

- Step 1: Identify the common factor in both terms.
- The terms are \( b^3 \) and \( b^2 \).
- The greatest common factor (GCF) of \( b^3 \) and \( b^2 \) is \( b^2 \).

- Step 2: Factor out the GCF.
- Write \( b^3 + b^2 \) as \( b^2(b + 1) \).

- Final Answer:
$$
b^3 + b^2 = b^2(b + 1)
$$

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6. \( 45m^7 - 27m^4 \)

- Step 1: Identify the common factor in both terms.
- The terms are \( 45m^7 \) and \( -27m^4 \).
- The greatest common factor (GCF) of the coefficients \( 45 \) and \( 27 \) is \( 9 \).
- The greatest common factor of the variables \( m^7 \) and \( m^4 \) is \( m^4 \).
- Therefore, the overall GCF is \( 9m^4 \).

- Step 2: Factor out the GCF.
- Write \( 45m^7 - 27m^4 \) as \( 9m^4(5m^3 - 3) \).

- Final Answer:
$$
45m^7 - 27m^4 = 9m^4(5m^3 - 3)
$$

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Summary of Answers:

1. \( 4b + 4c = 4(b + c) \)
2. \( 5m - 5n = 5(m - n) \)
3. \( 12b + 6c = 6(2b + c) \)
4. \( 15m - 9n = 3(5m - 3n) \)
5. \( b^3 + b^2 = b^2(b + 1) \)
6. \( 45m^7 - 27m^4 = 9m^4(5m^3 - 3) \)

Final Boxed Answers:

$$
\boxed{
\begin{aligned}
1. & \ 4(b + c) \\
2. & \ 5(m - n) \\
3. & \ 6(2b + c) \\
4. & \ 3(5m - 3n) \\
5. & \ b^2(b + 1) \\
6. & \ 9m^4(5m^3 - 3)
\end{aligned}
}
$$