Simplify: $(a + b) (2 a - 3 b + c) - (2 a - 3 b) (c)$ . [3 MARKS]

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Solution

Steps: 2 Marks
Answer: 1 Mark

$(a + b) (2 a - 3 b + c) - (2 a - 3 b) c$

$= [(a + b) (2 a - 3 b + c)] - [(2 a - 3 b) c]$

$= [2 a^{2} - 3 b a + a c + 2 a b - 3 b^{2} + b c] - [2 a c - 3 b c]$

$= 2 a^{2} - 3 b a + a c + 2 a b - 3 b^{2} + b c - 2 a c + 3 b c$

$= 2 a^{2} - 3 b^{2} - a b - a c + 4 b c$

The simplified expresion is
$= 2 a^{2} - 3 b^{2} - a b - a c + 4 b c$ .

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