Simplify the following expression and find the value when $x = 3, p = - 1 a n d q = - 2$
$p + q + p q x + 2 q$

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Solution

Step 1 : Simplify the given expression
Given expression is $p + q + p q x + 2 q$
On simplifying the expression,
$p + q + p q x + 2 q = p + p q x + (q + 2 q) . . . (g r o u p i n g t h e l i k e t e r m s) = p (1 + q x) + 3 q$
Step 2- Substitute the values of $x, p, q$ in simplified equation
now, putting the values of $x = 3, p = - 1 a n d q = - 2$ in simplified equation
we get,
$= (- 1) [1 + (- 2) (3)] + 3 (- 2) = (- 1) [1 + (- 6)] + (- 6) = (- 1) [1 - 5] - 6 = (- 1) (- 4) - 6 = (- 1 \times - 4) - 6 = 4 - 6 = - 2$
Hence, the required solution is $- 2$

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