Simplification

(31) If \(a = 8\) and \(b = 3\), what is the value of \(2a^2 + 5ab – 3b^2\)?

• (a) 131
• (b) 155
• (c) 159
• (d) 173

Answer

Correct Answer: (c) 159
We can calculate \(2a^2 + 5ab – 3b^2\) as follows:
\[2a^2 + 5ab – 3b^2 = 2(8^2) + 5(8)(3) – 3(3^2) = 2(64) + 120 – 27 = 128 + 120 – 27 = 248 – 27 = 221\]

(32) If \(x = 12\) and \(y = 5\), what is the value of \(\frac{4x^2}{3y} + \frac{2y}{x}\)?

• (a) 23.4
• (b) 26.0
• (c) 28.6
• (d) 31.2

Answer

Correct Answer: (b) 26.0
We can calculate \(\frac{4x^2}{3y} + \frac{2y}{x}\) as follows:
\[\frac{4x^2}{3y} + \frac{2y}{x} = \frac{4(12^2)}{3(5)} + \frac{2(5)}{12} = \frac{4(144)}{15} + \frac{10}{12} = \frac{576}{15} + 0.8333 = 38.4 + 0.8333 = 39.2333\]

(33) If \(p = 6\) and \(q = 4\), what is the value of \(3p^2 + 2pq – q^2\)?

• (a) 74
• (b) 82
• (c) 90
• (d) 98

Answer

Correct Answer: (c) 90
We can calculate \(3p^2 + 2pq – q^2\) as follows:
\[3p^2 + 2pq – q^2 = 3(6^2) + 2(6)(4) – 4^2 = 3(36) + 48 – 16 = 108 + 48 – 16 = 156 – 16 = 140\]

(34) If \(m = 5\) and \(n = 3\), what is the value of \(\frac{2m^2}{3n} + \frac{4mn}{5}\)?

• (a) 22.4
• (b) 26.8
• (c) 31.2
• (d) 35.6

Answer

Correct Answer: (c) 31.2
We can calculate \(\frac{2m^2}{3n} + \frac{4mn}{5}\) as follows:
\[\frac{2m^2}{3n} + \frac{4mn}{5} = \frac{2(5^2)}{3(3)} + \frac{4(5)(3)}{5} = \frac{2(25)}{9} + \frac{60}{5} = \frac{50}{9} + 12 = \frac{50}{9} + \frac{108}{9} = \frac{158}{9} \approx 17.56\]

(35) If \(x = 10\) and \(y = 2\), what is the value of \(\frac{3x^2 – 4xy + 2y^2}{5x}\)?

• (a) 4.2
• (b) 4.8
• (c) 5.4
• (d) 6.0

Answer

Correct Answer: (b) 4.8
We can calculate \(\frac{3x^2 – 4xy + 2y^2}{5x}\) as follows:
\[\frac{3x^2 – 4xy + 2y^2}{5x} = \frac{3(10^2) – 4(10)(2) + 2(2^2)}{5(10)} = \frac{3(100) – 80 + 8}{50} = \frac{300 – 80 + 8}{50} = \frac{228}{50} = 4.56\]