Add the following algebraic expressions.
a) $29 x, 5 x^{3}, - 13 x, - 9 x and - 17 x^{3}$
b) $- 5 x y + 7, 3 x y - 5 and - 2 x y + 9$
c) $2 a + 3 b - 4 a^{2} b and 4 a - 2 b + 3 a^{2} b$

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Solution

(a) $29 x, 5 x^{3}, - 13 x, - 9 x$ and $- 17 x^{3}$
$\Rightarrow (29 x) + (5 x^{3}) + (- 13 x) + (- 9 x) + (- 17 x^{3})$
$\Rightarrow 29 x + 5 x^{3} - 13 x - 9 x - 17 x^{3}$
$\Rightarrow - 12 x^{3} + 7 x$

(b) $- 5 x y + 7, 3 x y - 5$ and $- 2 x y + 9$
$\Rightarrow (- 5 x y + 7) + (3 x y - 5) + (- 2 x y + 9)$
$\Rightarrow - 5 x y + 7 + 3 x y - 5 - 2 x y + 9$
$\Rightarrow - 4 x y + 11$

(c) $2 a + 3 b - 4 a^{2} b$ and $4 a - 2 b + 3 a^{2} b$
$\Rightarrow (2 a + 3 b - 4 a^{2} b) + (4 a - 2 b + 3 a^{2} b)$
$\Rightarrow 2 a + 3 b - 4 a^{2} b + 4 a - 2 b + 3 a^{2} b$
$\Rightarrow 6 a + b - a^{2} b$ .

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