Simplify the expression $2 (a^{2} + a b) + 3 - a b$ and find its value when $a = 5$ and $b = - 3 .$

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Solution

Simplifying the given expression:
From the given details we get to know that $a = 5$ and $b = - 3 .$
We have,
$2 (a^{2} + a b) + 3 - a b$ $=$ $2 a^{2} + 2 a b + 3 - a b$
$=$ $2 a^{2} + a b + 3$
On substituting the value of $x$ in the above algebraic equation and simplifying we get
$2 a^{2} + a b + 3$ $=$ $(2 \times 5^{2}) + (5 \times (- 3)) + 3$
$= (2 \times 25) + (- 15) + 3$
$= 50 - 15 + 3$
$= 53 - 15$
$= 38$
Therefore, if $a = 5$ and $b = - 3 .$ then $2 a^{2} + a b + 3$ $= 38$ .

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