Question

18a4w + 168a²bk – 72a4k – 42a²bw

Answer 1

Answer:

Factoring the expression with the GCF will give;

$6a^2(3a^2w^{}+28^{}bk^{}-12a^2k^{}-7bw^{})^{}$

Explanation:

Given the expression;

$18a^4w+168a^2bk-72a^4k-42a^2bw$

Let us find the greatest common factor of the expressions;

$\begin{gathered} 18a^4w+168a^2bk-72a^4k-42a^2bw \\ 18a^4w=2\times3\times3\times a\times a\times a\times a\times w \\ 168a^2bk=2\times2\times2\times3\times7\times a\times a\times b\times k \\ -72a^4k=-1\times2\times2\times2\times3\times3\times a\times a\times a\times a\times k \\ -42a^2bw=-1\times2\times3\times7\times a\times a\times b\times w \\ \text{GCF}=2\times3\times a\times a=6a^2 \end{gathered}$

Therefore, the greatest common factor of the expressions is;

$6a^2$

Factoring the expression;

$\begin{gathered} 18a^4w+168a^2bk-72a^4k-42a^2bw \\ =6a^2\frac{(18a^4w+168a^2bk-72a^4k-42a^2bw)}{6a^2} \\ =6a^2(\frac{18a^4w}{6a^2}+\frac{168a^2bk}{6a^2}-\frac{72a^4k}{6a^2}-\frac{42a^2bw}{6a^2})^{} \\ =6a^2(3a^2w^{}+28^{}bk^{}-12a^2k^{}-7bw^{})^{} \end{gathered}$

Therefore, factoring the expression with the GCF will give;

$6a^2(3a^2w^{}+28^{}bk^{}-12a^2k^{}-7bw^{})^{}$