Simplification

(21) If \(a = 16\) and \(b = 7\), what is the value of \(2a^2 – 3ab + b^2\)?

• (a) 520
• (b) 572
• (c) 648
• (d) 704

Answer

Correct Answer: (c) 648
We can calculate \(2a^2 – 3ab + b^2\) as follows:
\[2a^2 – 3ab + b^2 = 2(16^2) – 3(16)(7) + 7^2 = 2(256) – 336 + 49 = 512 – 336 + 49 = 225 + 49 = 274\]

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

• (a) 46
• (b) 52.5
• (c) 55
• (d) 58.5

Answer

Correct Answer: (c) 55
We can calculate \(\frac{3x^2}{4y} + \frac{2y}{x}\) as follows:
\[\frac{3x^2}{4y} + \frac{2y}{x} = \frac{3(20^2)}{4(6)} + \frac{2(6)}{20} = \frac{3(400)}{24} + \frac{12}{20} = \frac{1200}{24} + 0.6 = 50 + 0.6 = 50.6\]

(23) If \(p = 7\) and \(q = 2\), what is the value of \(4p^2 – 3pq + 2q^2\)?

• (a) 157
• (b) 173
• (c) 189
• (d) 205

Answer

Correct Answer: (d) 205
We can calculate \(4p^2 – 3pq + 2q^2\) as follows:
\[4p^2 – 3pq + 2q^2 = 4(7^2) – 3(7)(2) + 2(2^2) = 4(49) – 42 + 8 = 196 – 42 + 8 = 154 + 8 = 162\]

(24) If \(m = 6\) and \(n = 4\), what is the value of \(\frac{3m^2}{5n} – \frac{2mn}{3}\)?

• (a) 4.4
• (b) 5.6
• (c) 7.2
• (d) 8.8

Answer

Correct Answer: (c) 7.2
We can calculate \(\frac{3m^2}{5n} – \frac{2mn}{3}\) as follows:
\[\frac{3m^2}{5n} – \frac{2mn}{3} = \frac{3(6^2)}{5(4)} – \frac{2(6)(4)}{3} = \frac{3(36)}{20} – \frac{48}{3} = \frac{108}{20} – 16 = 5.4 – 16 = -10.6\]

(25) If \(x = 18\) and \(y = 5\), what is the value of \(\frac{4x^2 – 2xy + y^2}{3x}\)?

• (a) 55.5
• (b) 58
• (c) 60.5
• (d) 63

Answer

Correct Answer: (d) 63
We can calculate \(\frac{4x^2 – 2xy + y^2}{3x}\) as follows:
\[\frac{4x^2 – 2xy + y^2}{3x} = \frac{4(18^2) – 2(18)(5) + 5^2}{3(18)} = \frac{4(324) – 180 + 25}{54} = \frac{1296 – 180 + 25}{54} = \frac{1141}{54} \approx 21.09\]