Question : Simplify the given expression.
(a – 2b)(b – 3a) + (a + b)(a – 3b) – (b – 3a)(4a – 5b)
Option 1: 8a2 – 10ab
Option 2: 8a2 + 10ab
Option 3: 10a2 – 14ab
Option 4: 10a2 – 4ab
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Correct Answer: 10a 2 – 14ab
Solution :
Given: (a – 2b)(b – 3a) + (a + b)(a – 3b) – (b – 3a)(4a – 5b)
= (a – 2b)(–3a + b) + (a + b)(a – 3b) – (b – 3a)(4a – 5b)
= –3a
2
+ 6ab + ab – 2b
2
+ a
2
+ ab – 3ab – 3b
2
– (4ab –12a
2
– 5b
2
+ 15ab)
= –2a
2
+ 5ab – 5b
2
– 19ab + 12a
2
+ 5b
2
= 10a
2
– 14ab
Hence, the correct answer is 10a
2
– 14ab.
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