Sure, let's solve the given expression step by step.
Given:
[tex]\[
\frac{30g^3 + 15g^2}{5g}
\][/tex]
1. Expression Expansion:
First, let's look at the numerator [tex]\(30g^3 + 15g^2\)[/tex].
2. Factor Out Common Terms in the Numerator:
Notice that both terms in the numerator have a common factor of [tex]\(15g^2\)[/tex]:
[tex]\[
30g^3 + 15g^2 = 15g^2(2g + 1)
\][/tex]
3. Rewrite the Fraction:
Now, rewrite the fraction using the factored form of the numerator:
[tex]\[
\frac{15g^2(2g + 1)}{5g}
\][/tex]
4. Simplify the Fraction:
Divide both the numerator and the denominator by the common term [tex]\(5g\)[/tex]:
[tex]\[
\frac{15g^2(2g + 1)}{5g} = \frac{15g^2}{5g} \times (2g + 1)
\][/tex]
5. Simplify the Terms:
[tex]\(\frac{15g^2}{5g}\)[/tex] simplifies to:
[tex]\[
\frac{15}{5} \cdot \frac{g^2}{g} = 3g
\][/tex]
6. Final Expression:
Multiply the simplified term [tex]\(3g\)[/tex] by the remaining binomial [tex]\((2g + 1)\)[/tex]:
[tex]\[
3g \cdot (2g + 1) = 3g(2g + 1)
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
3g(2g + 1)
\][/tex]
