Question

4a^2b^3-24a^3b

Answer 1

We need to factor;
\[4a^{2}b^{3}−24a^{3}b\]
First start by finding what 24 and 4 have in common..Well, -24/4=-6 and 4*-6=-24, so this is what we have so far;
\[4(−6)\]
But we still have to deal with the variables and exponents. Since we are dealing with bases of a and b, all we have to do is split them up since exponents with the same bases are just combined with addition;
\[x^{2}x^{3}=x^{5}\]
Which gives us;
\[4a^{2}b(b^{2}−6a)\]
And using the distributive property of multiplication;
\[a^{2}b×b^{2}=a^{2}b^{3}\]
and
\[a^{2}b×a=a^{3}b\]
So,
\[4a^{2}b×b^{2}=4a^{2}b^{3}\]
and
\[4a^{2}b×−6a=−24a^{3}b\]