Question

What is the simplest form of this expression

Answer 1

-9m[(m+1)(m^2-m+1)]

Explanation:

Given

-m(4m^(3 )+9 )-5m^4

The simplest form means the most factorized form of an expression

Multiplying –m into the bracket

=-4m^3.m-9m- 5m^4

= -4m^(4 )-9m- 5m^4

= -9m^4-9m

Taking -9m as common factor

= -9m( m^3+1)

m^3+1 can further be factorized

Using the cube’s formula

a^3+ b^3=(a+b)(a^(2 )+ b^2-ab)

So,

m^3+ 1=(m+1)(m^(2 )+ 1-m)

So

= -9m[(m+1)(m^2-m+1)]

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