Assignment 5: Exercise on Algebraic Expressions

solve the questions, showing your work, and submit it to the W1: Assignment 5 Dropbox. Your facilitator will discuss questions, which seem troublesome, in this Discussion Area.

1. Simplify: 4[a – b(2 + 3a)] – 3a[2+b(4 – a)]
2. Simplify: (7x² –  2y + z) + (3y –  z) + (4x² – 6y)
3. Simplify: (8x² – xy + 4y²) – (12x² – y² + 7xy)
4. Simplify: (12x²y² – 15xy²)/(3xy)
5. Simplify: 5x[(3x² + x – 4) + (9x² – 6x)/(3x)]
6. Simplify: 8 – {3x + 9y – (2x – y) + 8x + 5y}
7. If P = 2y – 6xy – 3x and Q = 4 – 5y, find the value of 2P – 3Q.
8. A woman buys three board games for $107.10, including tax.  If each board game cost $34, what was the sales tax rate?
9. Sandy has $3.25 in change. She has five more dimes than quarters but twice as many nickels as dimes. Express the given information as an algebraic expression and simplify. [You are not required to solve the problem.]
10. Jim’s nephew owns a triangular plot of land. The perimeter fence that surrounds the land measures 121 feet. The shortest side is 15 feet longer than one-half of the longest side. The second longest side is 4 feet shorter than the longest side.  What is the length of each side?