Question

b^2c^3+8bc^4+12c^5 factorize​

Answer 1

Answer:

c³ (2c + b ) ( 6c + b )

Step-by-step explanation:

Given--->

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b² c³ + 8 b c⁴ + 12 c⁵

To find--->

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factorize given exression

Solution--->

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b²c³ + 8 b c⁴ + 12 c⁵

We can take common c³ from all terms

=c³(b² + 8 b c + 12 c² )

rearranging terms

=c³ (12c² + 8 b c + b² )

Now we factorize it by splitting the middle term

we break 12 in to two parts whose sum is 8 which are 6 and 2

=c³ {12 c² +(6 + 2)bc + b² }

=c³ (12c² + 6bc + 2bc + b² )

=c³ {6c(2c + b) + b(2c + b)}

=c³ (2c + b) (6 c + b)

Additional information--->

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1) a² - b² = (a + b ) (a - b )

2)(a + b )² = a² + b² + 2ab

3)(a - b)²=a² + b² - 2ab

4)(a+b)³ =a³ + b³ +3a b (a + b)

5)(a - b)³=a³ - b³ -3a b (a - b)