Write the final factorization for each problem. 12a^3 + 20a^2b - 9ab^2 - 15b^3

Write the final factorization for each problem. 12a^3 + 20a^2b - 9ab^2 - 15b^3

Question
Polynomial factorization
asked 2021-02-25
Write the final factorization for each problem.
\(\displaystyle{12}{a}^{{3}}+{20}{a}^{{2}}{b}-{9}{a}{b}^{{2}}-{15}{b}^{{3}}\)

Answers (1)

2021-02-26
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:\(\displaystyle{\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}\)
0

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