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Question :
(a² – a – b)(a² – a – 2)
Let us assume :
a² – a → x
b → y
2 → z
Solution :
(x + y)(x + z)
x² + (y + z)x + y•z
By putting the values we get :
(a² – a)² + {– b +(– 2)}(a² – a) + (–b) × (–2)
Using identity (a – b)² → a² – 2ab + b² for (a² – a)² we get,
a⁴ – 2•a²•a + a² ( b + 2)(a² – a) + 2b
a⁴ – 2a³ + a² – b(a² – a) – 2(a² – a) + 2b
a⁴ – 2a³ + a² – a²b + ab – 2a² + 2a + 2b
Now we have to assemble the values
a⁴ – 2a³ + a² – 2a² – a²b + 2b + ab + 2a
a³(a – 2) + a²(a – 2) – b(a² – 2) + a(b + 2)
(a – 2)(a³ + a²) – b(a² – 2) + a(b + 2)
- So the answer is (a – 2)(a³ + a²) – b(a² – 2) + a(b + 2)
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