Simplification

(26) If \(a = 12\) and \(b = 6\), what is the value of \(3a^2 + 4ab + 2b^2\)?

• (a) 920
• (b) 1024
• (c) 1104
• (d) 1216

Answer

Correct Answer: (c) 1104
We can calculate \(3a^2 + 4ab + 2b^2\) as follows:
\[3a^2 + 4ab + 2b^2 = 3(12^2) + 4(12)(6) + 2(6^2) = 3(144) + 288 + 72 = 432 + 288 + 72 = 792 + 72 = 864\]

(27) If \(x = 15\) and \(y = 3\), what is the value of \(\frac{2x^2}{5y} – \frac{3y}{x}\)?

• (a) 18.6
• (b) 20.4
• (c) 22.2
• (d) 24.0

Answer

Correct Answer: (b) 20.4
We can calculate \(\frac{2x^2}{5y} – \frac{3y}{x}\) as follows:
\[\frac{2x^2}{5y} – \frac{3y}{x} = \frac{2(15^2)}{5(3)} – \frac{3(3)}{15} = \frac{2(225)}{15} – \frac{9}{15} = \frac{450}{15} – 0.6 = 30 – 0.6 = 29.4\]

(28) If \(p = 9\) and \(q = 4\), what is the value of \(5p^2 – 2pq + 3q^2\)?

• (a) 293
• (b) 325
• (c) 361
• (d) 397

Answer

Correct Answer: (d) 397
We can calculate \(5p^2 – 2pq + 3q^2\) as follows:
\[5p^2 – 2pq + 3q^2 = 5(9^2) – 2(9)(4) + 3(4^2) = 5(81) – 72 + 48 = 405 – 72 + 48 = 381 + 48 = 429\]

(29) If \(m = 10\) and \(n = 2\), what is the value of \(\frac{4m^2}{5n} – \frac{3mn}{2}\)?

• (a) 43
• (b) 49
• (c) 55
• (d) 61

Answer

Correct Answer: (d) 61
We can calculate \(\frac{4m^2}{5n} – \frac{3mn}{2}\) as follows:
\[\frac{4m^2}{5n} – \frac{3mn}{2} = \frac{4(10^2)}{5(2)} – \frac{3(10)(2)}{2} = \frac{4(100)}{10} – 30 = 40 – 30 = 10\]

(30) If \(x = 14\) and \(y = 7\), what is the value of \(\frac{3x^2 – 2xy + y^2}{4x}\)?

• (a) 30.25
• (b) 31.5
• (c) 33.75
• (d) 36

Answer

Correct Answer: (b) 31.5
We can calculate \(\frac{3x^2 – 2xy + y^2}{4x}\) as follows:
\[\frac{3x^2 – 2xy + y^2}{4x} = \frac{3(14^2) – 2(14)(7) + 7^2}{4(14)} = \frac{3(196) – 196 + 49}{56} = \frac{588 – 196 + 49}{56} = \frac{441}{56} \approx 7.875\]