Question

If a = 2 and b = 3, find the value of
(i) a + b
(ii) a² + ab
(ii) ab − a²
(iv) 2a − 3b
(v) 5a² − 2ab
(vi) a³ − b³

Answer 1

(i) a+b
Substituting a = 2 and b = 3 in the given expression:
2+3 = 5

(ii) ${\mathrm{a}}^2+\mathrm{ab}$
Substituting a = 2 and b = 3 in the given expression:
$$\begin{gathered} (2{)}^2+(2\times 3)=4+6 \\ =10 \end{gathered}$$

(iii) $\mathrm{ab}-{\mathrm{a}}^2$
Substituting a = 2 and b = 3 in the given expression:
$$\begin{gathered} (2\times 3)-(2{)}^2=6-4 \\ =2 \end{gathered}$$

(iv) 2a-3b
Substituting a = 2 and b = 3 in the given expression:
$$\begin{gathered} (2\times 2)-(3\times 3)=4-9 \\ =-5 \end{gathered}$$

(v) $5{\mathrm{a}}^2-2\mathrm{ab}$
Substituting a=2 and b=3 in the given expression:
$$\begin{gathered} 5\times (2{)}^2-2\times 2\times 3=5\times 4-12=20-12 \\ =8 \end{gathered}$$

(vi) ${\mathrm{a}}^3-{\mathrm{b}}^3$
Substituting a=2 and b=3 in the given expression:
$$\begin{gathered} 2^3-3^3=2\times 2\times 2-3\times 3\times 3=8-27 \\ =-19 \end{gathered}$$