Question

factor completely 16a^3b^7 + 2a^6b^4 - 22a^4b^5.
2(8a^3b^7 + a^6b^4 - 11a^4b^5)
2a^3b^4(8b^3 + a^3 - 11ab)
a^3b^4(16b^3 + 2a^3 - 22ab)
8b^3 + a^3 - 11ab

Explanation:

Step1: Find GCF of coefficients

The coefficients are 16, 2, and - 22. The greatest - common factor of 16, 2, and - 22 is 2.

Step2: Find GCF of variables with 'a'

For the 'a' terms \(a^{3},a^{6},a^{4}\), the GCF of the exponents 3, 6, and 4 is \(a^{3}\) (since \(a^{3}\) is the lowest power of 'a' among them).

Step3: Find GCF of variables with 'b'

For the 'b' terms \(b^{7},b^{4},b^{5}\), the GCF of the exponents 7, 4, and 5 is \(b^{4}\) (since \(b^{4}\) is the lowest power of 'b' among them).

Step4: Factor out the GCF

The GCF of the entire expression \(16a^{3}b^{7}+2a^{6}b^{4}-22a^{4}b^{5}\) is \(2a^{3}b^{4}\).
\[

$$\begin{align*} 16a^{3}b^{7}+2a^{6}b^{4}-22a^{4}b^{5}&=2a^{3}b^{4}(8b^{3}+a^{3}-11ab) \end{align*}$$

\]

Answer:

B. \(2a^{3}b^{4}(8b^{3}+a^{3}-11ab)\)