4) If $$ a+b=a b=5 $$, then $$ a^{2} b+a b^{2}=\ldots $$ $$ (30,25,15,10) $$

Question

UpStudy AI · Accepted Answer

Given the equations $$ a + b = 5 $$ and $$ ab = 5 $$, we want to find the value of $$ a^2 b + ab^2 $$.

We can factor $$ a^2 b + ab^2 $$ as follows:

$$
a^2 b + ab^2 = ab(a + b)
$$

Now, we can substitute the known values into this expression. We know that $$ ab = 5 $$ and $$ a + b = 5 $$:

$$
a^2 b + ab^2 = ab(a + b) = 5 \cdot 5 = 25
$$

Thus, the value of $$ a^2 b + ab^2 $$ is

$$
\boxed{25}
$$
$$ a^2 b + ab^2 = 25 $$

4) If \( a+b=a b=5 \), then \( a^{2} b+a b^{2}=\ldots \) \( (30,25,15,10) \)