**Polynomials Unit 6 - Quest**
**Algebra 1**
**Name:** Delaltia Duncan

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**Instructions:**
Show all your work clearly. Also, give the type and degree of your solution.

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**Problems 1 and 2:**
Find the area and perimeter.

1. [Illustration showing a figure with a length of 70 ft]

2. **Expression:**
\[
6x^2 + 2
\]
\[
2x^3 - 3
\]

**Area Formula:** \[A = L \cdot W\] (Foil)
\[
A = 6x^2 + 2(2x^2 - 3)
\]
**Simplify:**
\[
12x^4 - 18x^2 + 4x^2 - 6
\]
\[
12x^4 - 14x^2 - 6
\]

**Type:** Trinomial
**Degree:** 4

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**Problem 3:**
Simplify:
\[
\left(2x^2y^7\right)^3\left(3x^4y^2\right)^{-3}\left(27x^5y^{10}\right)^0
\]
\[
2^3x^6y^{21} \cdot 3^{-3}x^{-12}y^{-6}
\]
\[
= 8x^6y^{21}
\]
\[
27x^{12}y^6
\]

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**Problem 4:**
Find the area using the expression:
\[A = L \cdot W\]
**Expression:**
\[
\left(3xy^2\right)^2 \cdot \left(2x^2\right)^4
\]
**Simplify:**
\[
3^2x^2y^4 \cdot 2^4x^8
\]
\[
= 9x^2y^4 \cdot 16x^8
\]