Step 1

GCF of \(\displaystyle{12}{a}^{{3}}{\quad\text{and}\quad}{20}{a}^{{2}}{b}{i}{s}={4}{a}^{{2}}\)

GCF of \(\displaystyle-{9}{a}{b}^{{2}}{\quad\text{and}\quad}-{15}{b}^{{3}}{i}{s}=-{3}{b}^{{2}}\)

Factor out \(\displaystyle{4}{a}^{{2}}\) from the first two terms and then factor out \(\displaystyle-{3}{b}^{{2}}\) from the last two terms.

\(\displaystyle{12}{a}^{{3}}+{20}{a}^{{2}}{b}-{9}{a}{b}^{{2}}-{15}{b}^{{3}}\)

\(\displaystyle={4}{a}^{{2}}{\left({3}{a}+{5}{b}\right)}-{3}{b}^{{2}}{\left({3}{a}+{5}{b}\right)}\)

Step 2

Then we can factor out (3a+5b) from both terms.

\(\displaystyle{4}{a}^{{2}}{\left({3}{a}+{5}{b}\right)}-{3}{b}^{{2}}{\left({3}{a}+{5}{b}\right)}\)

\(\displaystyle={\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}\)

Result:\(\displaystyle{\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}\)

GCF of \(\displaystyle{12}{a}^{{3}}{\quad\text{and}\quad}{20}{a}^{{2}}{b}{i}{s}={4}{a}^{{2}}\)

GCF of \(\displaystyle-{9}{a}{b}^{{2}}{\quad\text{and}\quad}-{15}{b}^{{3}}{i}{s}=-{3}{b}^{{2}}\)

Factor out \(\displaystyle{4}{a}^{{2}}\) from the first two terms and then factor out \(\displaystyle-{3}{b}^{{2}}\) from the last two terms.

\(\displaystyle{12}{a}^{{3}}+{20}{a}^{{2}}{b}-{9}{a}{b}^{{2}}-{15}{b}^{{3}}\)

\(\displaystyle={4}{a}^{{2}}{\left({3}{a}+{5}{b}\right)}-{3}{b}^{{2}}{\left({3}{a}+{5}{b}\right)}\)

Step 2

Then we can factor out (3a+5b) from both terms.

\(\displaystyle{4}{a}^{{2}}{\left({3}{a}+{5}{b}\right)}-{3}{b}^{{2}}{\left({3}{a}+{5}{b}\right)}\)

\(\displaystyle={\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}\)

Result:\(\displaystyle{\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}\)