Add: [2 MARKS]

(i) $3 x^{3} - 5 x^{2} + 8 x + 10$ ,
$15 x^{3} - 6 x - 23$ and
$9 x^{2} - 4 x + 15$

(ii) $3 a b^{2} - 2 b^{2} + a^{2}$ ,
$5 a^{2} b - 2 a b^{2} - 3 a^{2}$ and
$8 a^{2} - 5 b^{2}$

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Solution

Each Point: 1 Mark

(i) $(3 x^{3} - 5 x^{2} - + 8 x + 10) + (15 x^{3} - 6 x - 23) + (9 x^{2} - 4 x + 15)$

$= 3 x^{3} - 5 x^{2} + 8 x + 10 + 15 x^{3} - 6 x - 23 + 9 x^{2} - 4 x + 15$

Bringing like terms together, we get,

$= 3 x^{3} + 15 x^{3} - 5 x^{2} + 9 x^{2} + 8 x - 6 x - 4 x + 10 - 23 + 15$

$= 18 x^{3} + 4 x^{2} - 2 x + 2$

(ii) $(3 a b^{2} - 2 b^{2} + a^{2}) + (5 a^{2} b - 2 a b^{2} - 3 a^{2}) + (8 a^{2} - 5 b^{2})$

$= 3 a b^{2} - 2 b^{2} + a^{2} + 5 a^{2} b - 2 a b^{2} - 3 a^{2} + 8 a^{2} - 5 b^{2}$

Bringing like terms together, we get,

$= 3 a b^{2} - 2 a b^{2} - 2 b^{2} - 5 b^{2} + a^{2} - 3 a^{2} + 8 a^{2} + 5 a^{2} b$

$= 5 a^{2} b + a b^{2} + 6 a^{2} - 7 b^{2}$

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