Evaluating Algebraic Expressions

Evaluating algebraic expressions is the process of replacing variables with specific values and then simplifying.

In the expression $a+b,$ the letters $a$ and $b$ are called variables. If $a=-4$ and $b=7,$ then $a+b = -4+7 = 3.$

Evaluate $x^2+13$ when $x = -3$.

Answer

Putting $x=-3$ in the given expression, we have:

$$\begin{aligned} x^2 + 13 &= (-3)^2 + 13 \\ &= 9+13 \\ &=22 . \end{aligned}$$

Thus, the answer is 22.

Evaluate $5m+4n$ when $m = 3$ and $n = -2.$

Answer

We have

$$\begin{aligned} 5m + 4n =& 5 \times m + 4 \times n \\ =& 5 \times 3 + 4 \times (-2) \\ =& 15 + (-8) \\ =& 15 - 8 \\ =& 7. \end{aligned}$$

Thus, the answer is 7.

Evaluate $\displaystyle{\sqrt{p(q-1)(r+1)}}$ when $p = 4,$ $q = -3,$ and $r=-5.$

Answer

We have

$$\begin{aligned} \sqrt{p(q-1)(r+1)} =& \sqrt{4 \times (-3-1) \times (-5+1)} \\ =& \sqrt{4 \times (-4) \times (-4)} \\ =& \sqrt{4 \times 16} \\ =& \sqrt{64} \\ =& 8. \end{aligned}$$

Thus, the answer is 8.

Evaluate $10x + 9x + 8x ..... + x$ , where $x = 4$

Answer

We have

$$\begin{aligned} 10x + 9x + 8x ..... + x =& x ( 10 + 9 + 8 .... + 1 ) \\ =& x ( 55 ) \\ =& (4) 55 \qquad (\text{since }x=4)\\ =& 220 . \end{aligned}$$

So, the answer is $220.$