Simplification

(16) If \(a = 18\) and \(b = 5\), what is the value of \(4a^2 + 3ab – 2b^2\)?

• (a) 823
• (b) 1180
• (c) 1372
• (d) 1536

Answer

Correct Answer: (b) 1180
We can calculate \(4a^2 + 3ab – 2b^2\) as follows:
\[4a^2 + 3ab – 2b^2 = 4(18^2) + 3(18)(5) – 2(5^2) = 4(324) + 270 – 50 = 1296 + 270 – 50 = 1516\]

(17) If \(x = 15\) and \(y = 4\), what is the value of \(\frac{5x^2}{3y} – \frac{2y}{x}\)?

• (a) 64
• (b) 72
• (c) 80
• (d) 88

Answer

Correct Answer: (c) 80
We can calculate \(\frac{5x^2}{3y} – \frac{2y}{x}\) as follows:
\[\frac{5x^2}{3y} – \frac{2y}{x} = \frac{5(15^2)}{3(4)} – \frac{2(4)}{15} = \frac{5(225)}{12} – \frac{8}{15} = \frac{1125}{12} – \frac{8}{15} = 93.75 – 0.5333 = 93.2167\]

(18) If \(p = 8\) and \(q = 3\), what is the value of \(3p^2 + 2pq + q^2\)?

• (a) 165
• (b) 188
• (c) 204
• (d) 217

Answer

Correct Answer: (d) 217
We can calculate \(3p^2 + 2pq + q^2\) as follows:
\[3p^2 + 2pq + q^2 = 3(8^2) + 2(8)(3) + 3^2 = 3(64) + 48 + 9 = 192 + 48 + 9 = 249\]

(19) If \(m = 9\) and \(n = 7\), what is the value of \(\frac{2m^2}{5n} – \frac{mn}{3}\)?

• (a) 9.4
• (b) 12.1
• (c) 15.2
• (d) 18.7

Answer

Correct Answer: (c) 15.2
We can calculate \(\frac{2m^2}{5n} – \frac{mn}{3}\) as follows:
\[\frac{2m^2}{5n} – \frac{mn}{3} = \frac{2(9^2)}{5(7)} – \frac{9(7)}{3} = \frac{2(81)}{35} – \frac{63}{3} = \frac{162}{35} – 21 = 4.6286 – 21 = -16.3714\]

(20) If \(x = 14\) and \(y = 6\), what is the value of \(\frac{3x^2 – 2xy + y^2}{4x}\)?

• (a) 23.5
• (b) 25.75
• (c) 29.25
• (d) 31.5

Answer

Correct Answer: (b) 25.75
We can calculate \(\frac{3x^2 – 2xy + y^2}{4x}\) as follows:
\[\frac{3x^2 – 2xy + y^2}{4x} = \frac{3(14^2) – 2(14)(6) + 6^2}{4(14)} = \frac{3(196) – 168 + 36}{56} = \frac{588 – 168 + 36}{56} = \frac{456}{56} = 8.1429\]