1) $$ \left(4 v^{4}+16 v^{3}+16 v^{2}\right) \div 4 v^{2} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{4v^{4} + 16v^{3} + 16v^{2}}{4v^{2}}
$$

**Step 1: Factor out the common term in the numerator**

Notice that each term in the numerator has a common factor of $$4v^{2}$$:

$$
4v^{4} + 16v^{3} + 16v^{2} = 4v^{2}(v^{2} + 4v + 4)
$$

**Step 2: Divide the factored numerator by the denominator**

$$
\frac{4v^{2}(v^{2} + 4v + 4)}{4v^{2}}
$$

The $$4v^{2}$$ in the numerator and the denominator cancel out:

$$
v^{2} + 4v + 4
$$

**Step 3: (Optional) Factor the quadratic expression**

The quadratic $$v^{2} + 4v + 4$$ can be factored further:

$$
v^{2} + 4v + 4 = (v + 2)^2
$$

**Final Answer:**

$$
v^{2} + 4v + 4
$$

Alternatively, factored form:

$$
(v + 2)^2
$$
The simplified form of the expression is $$ v^{2} + 4v + 4 $$ or $$ (v + 2)^2 $$.

1) \( \left(4 v^{4}+16 v^{3}+16 v^{2}\right) \div 4 v^{2} \)