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 \( x = -3 \).

Putting \(x=-3\) in the given expression, we have:

\[ \begin{align} x^2 + 13 &= (-3)^2 + 13 \\ &= 9+13 \\ &=22 . \end{align}\]

Thus, the answer is 22.

Evaluate \(5m+4n \) when \( m = 3 \) and \(n = -2.\)

We have

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

Thus, the answer is 7.

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

We have

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

Thus, the answer is 8.

Evaluate \( 10x + 9x + 8x ..... + x\) , where \( x = 4 \)

We have

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

So, the answer is \(220.\)