Simplification

user November 19, 2023

(6) If \(p = 10\) and \(q = 3\), what is the value of \(2p^3 – 4q^2\)?

(a) 186
(b) 214
(c) 236
(d) 254

Correct Answer: (d) 254
We can calculate \(2p^3 – 4q^2\) as follows:
\[2p^3 – 4q^2 = 2(10^3) – 4(3^2) = 2(1000) – 4(9) = 2000 – 36 = 1964\]

(7) If \(m = 8\) and \(n = 5\), what is the value of \(\frac{3m^2}{2} + \frac{n}{4}\)?

(a) 34
(b) 37.5
(c) 42
(d) 46.5

Correct Answer: (b) 37.5
We can calculate \(\frac{3m^2}{2} + \frac{n}{4}\) as follows:
\[\frac{3m^2}{2} + \frac{n}{4} = \frac{3(8^2)}{2} + \frac{5}{4} = \frac{3(64)}{2} + \frac{5}{4} = 96 + 1.25 = 97.25\]

(8) If \(x = 6\) and \(y = 7\), what is the value of \(\frac{2x + 3y}{xy}\)?

(a) 2.25
(b) 2.5
(c) 3
(d) 3.5

Correct Answer: (c) 3
We can calculate \(\frac{2x + 3y}{xy}\) as follows:
\[\frac{2x + 3y}{xy} = \frac{2(6) + 3(7)}{6 \cdot 7} = \frac{12 + 21}{42} = \frac{33}{42} = \frac{11}{14} = 3\]

(9) If \(a = 12\) and \(b = 4\), what is the value of \(\frac{a^2 – b^2}{a + b}\)?

(a) 20
(b) 16
(c) 14
(d) 10

Correct Answer: (a) 20
We can calculate \(\frac{a^2 – b^2}{a + b}\) as follows:
\[\frac{a^2 – b^2}{a + b} = \frac{12^2 – 4^2}{12 + 4} = \frac{144 – 16}{16} = \frac{128}{16} = 8 \cdot \frac{16}{16} = 8 \cdot 1 = 8\]

(10) If \(x = 9\) and \(y = 2\), what is the value of \(x^2 + 2xy + y^2\)?