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Original Question
How would you rewrite the expression 24ab^2c+18a^3b by factoring out the GCF? (1 point)Asked by burnout
How would you rewrite the expression 6a2+12a5
by factoring out the GCF?
by factoring out the GCF?
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Answered by
GPT-4o mini
To rewrite the expression \( 6a^2 + 12a^5 \) by factoring out the greatest common factor (GCF), we first need to determine the GCF of the coefficients and the variables.
1. **Coefficients:** The GCF of the coefficients 6 and 12 is 6.
2. **Variables:** The GCF of \( a^2 \) and \( a^5 \) is \( a^2 \), since the lowest power of \( a \) present in the terms is \( a^2 \).
Now, we can factor out the GCF, which is \( 6a^2 \):
\[
6a^2 + 12a^5 = 6a^2(1 + 2a^3)
\]
Thus, the expression \( 6a^2 + 12a^5 \) factored out by the GCF is:
\[
6a^2(1 + 2a^3)
\]
1. **Coefficients:** The GCF of the coefficients 6 and 12 is 6.
2. **Variables:** The GCF of \( a^2 \) and \( a^5 \) is \( a^2 \), since the lowest power of \( a \) present in the terms is \( a^2 \).
Now, we can factor out the GCF, which is \( 6a^2 \):
\[
6a^2 + 12a^5 = 6a^2(1 + 2a^3)
\]
Thus, the expression \( 6a^2 + 12a^5 \) factored out by the GCF is:
\[
6a^2(1 + 2a^3)
\]
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