Question

solve the following m³-8​

Answer 1

Answer:

Required factorized value of m^3 - 8 is ( m - 2 )( m^2 + 2m + 4 ).

Step-by-step explanation:

Given polynomial is m^3 - 8 . If we observe the situation, we can observe that 8 is the cube of 2( since 2 x 2 x 2 = 8 ), and thus, both the terms present are the cubes of any other number, and, are in relation with a negative sign.

= > m^3 - 8

= > m^3 - ( 2 x 2 x 2 )

= > m^3 - 2^3

From the properties of factorization : -

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

Therefore,

= > ( m - 2 ){ ( m )^2 + ( m x 2 ) + ( 2 )^2 }

= > ( m - 2 ){ m^2 + 2m + 4 }

Hence the required factorized value of m^3 - 8 is ( m - 2 )( m^2 + 2m + 4 ).