factorise
11. a3 - 125 - 2a + 10
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Answer:
The given expression is:
a^3a
3
- 125 - 2a + 10
We have to find the factorisation of a^3a
3
- 125 - 2a + 10.
Solution:
∴ a^3a
3
- 125 - 2a + 10
= a^3a
3
- 5^35
3
- 2a + 10
Using the algebraic identity:
a^3a
3
- b^3b
3
= (a - b)( a^2a
2
+ ab + b^2b
2
)
= (a - 5)( a^2a
2
+ 5a + 5^25
2
) - 2a + 10
= (a - 5)( a^2a
2
+ 5a + 2525 ) - 2(a - 5)
Taking (a - 5) as common, we get
= (a - 5)[( a^2a
2
+ 5a + 2525 ) - 2]
= (a - 5)( a^2a
2
+ 5a + 2525 - 2)
= (a - 5)( a^2a
2
+ 5a + 23)
∴ The factorisation of a^3a
3
- 125 - 2a + 10 = (a - 5)( a^2a
2
+ 5a + 23)
Thus, the factorisation of a^3a
3
- 125 - 2a + 10 is "(a - 5)( a^2a
2
+ 5a + 23)".
Step-by-step explanation:
Hope this helped
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