(6) $$ \quad(-2 x-4 y)(3 x+5 y) \cdot 2 $$ (8) $$ \quad\left(4 b^{2}+5 c^{2}\right)\left(-b^{3}+2 c^{5}\right) $$

Question

UpStudy AI · Accepted Answer

Let's expand and simplify each of the given expressions step by step.

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### Problem (6)

$$
(-2x - 4y)(3x + 5y) \cdot 2
$$

**Step 1: Expand the binomials**

$$
\begin{align*}
(-2x)(3x) &= -6x^2 \
(-2x)(5y) &= -10xy \
(-4y)(3x) &= -12xy \
(-4y)(5y) &= -20y^2
\end{align*}
$$

Combine the like terms:

$$
-6x^2 - 10xy - 12xy - 20y^2 = -6x^2 - 22xy - 20y^2
$$

**Step 2: Multiply by 2**

$$
2 \cdot (-6x^2 - 22xy - 20y^2) = -12x^2 - 44xy - 40y^2
$$

**Final Answer for Problem (6):**

$$
-12x^2 - 44xy - 40y^2
$$

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### Problem (8)

$$
(4b^{2} + 5c^{2})(-b^{3} + 2c^{5})
$$

**Step 1: Expand the binomials**

$$
\begin{align*}
4b^{2} \cdot (-b^{3}) &= -4b^{5} \
4b^{2} \cdot 2c^{5} &= 8b^{2}c^{5} \
5c^{2} \cdot (-b^{3}) &= -5b^{3}c^{2} \
5c^{2} \cdot 2c^{5} &= 10c^{7}
\end{align*}
$$

**Step 2: Combine all terms**

$$
-4b^{5} - 5b^{3}c^{2} + 8b^{2}c^{5} + 10c^{7}
$$

**Final Answer for Problem (8):**

$$
-4b^{5} - 5b^{3}c^{2} + 8b^{2}c^{5} + 10c^{7}
$$

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These are the fully expanded forms of the given expressions.
$$ -12x^2 - 44xy - 40y^2 $$ $$ -4b^{5} - 5b^{3}c^{2} + 8b^{2}c^{5} + 10c^{7} $$

(6)
(8)

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