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Multiplication of a Binomial by a Monomial

Question 5dSu...

Question

Question 5(d)
Substract: $3 a (a + b + c) - 2 b (a - b + c) f r o m 4 c (- a + b + c) .$

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Solution

$4 c (- a + b + c) - [3 a (a + b + c) - 2 b (a - b + c)]$
$= - 4 a c + 4 b c + 4 c^{2} - [3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} - 2 b c]$
$= - 4 a c + 4 b c + 4 c^{2} - [3 a^{2} + 2 b^{2} + 3 a b - 2 b c + 3 a c - 2 a b]$
$= - 4 a c + 4 b c + 4 c^{2} - [3 a^{2} + 2 b^{2} + a b + 3 a c - 2 b c]$
$= - 4 a c + 4 b c + 4 c^{2} - 3 a^{2} - 2 b^{2} - a b - 3 a c + 2 b c$
$= - 3 a^{2} - 2 b^{2} + 4 c^{2} - a b + 4 b c + 2 b c - 4 a c - 3 a c$
$= - 3 a^{2} - 2 b^{2} + 4 c^{2} - a b + 6 b c - 7 a c$

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

4 c (- a + b + c)

Question 5(d)
Substract: $3 a (a + b + c) - 2 b (a - b + c) f r o m 4 c (- a + b + c) .$

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Add:

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

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