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Addition and Subtraction of Algebraic Expressions

Add: 14x + 10...

Question

Add: $14 x + 10 y - 12 x y - 13, 18 - 7 x - 10 y + 8 x y, 4 x y$

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Solution

We have to add : $14 x + 10 y - 12 x y - 13, 18 - 7 x - 10 y + 8 x y, 4 x y$
On combining the like terms and adding them, we get
$\begin{array}{rcl} = & 14 x + 10 y - 12 x y - 13 + (18 - 7 x - 10 y + 8 x y) + 4 x y \\ = & 14 x + 10 y - 12 x y - 13 + 18 - 7 x - 10 y + 8 x y + 4 x y \\ = & 14 x - 7 x + 10 y - 10 y - 12 x y + 8 x y + 4 x y - 13 + 18 \\ = & x (14 - 7) + y (10 - 10) + x y (- 12 + 8 + 4) + (- 13 + 18) \\ = & x (7) + y (0) + x y (0) + (5) \\ = & 7 x + 5 \end{array}$
Hence, On adding $14 x + 10 y - 12 x y - 13, 18 - 7 x - 10 y + 8 x y, 4 x y$ we get $7 x + 5$ .

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