Question

please answer the question

Answer 1

m^3 - 12m^2 + 48m + 64

Term = m^3 , -12m^2 , 48m , 64

Factors = m×m×m , -12×m×m , 48×m , 64

Hope it helps you!!

Answer 2

Step-by-step explanation:

Given :-

The expression is m^3 -12m^2 +48m-64

To find:-

Factorise the expression m^3 -12m^2 +48m-64

Solution:-

Given expression is m^3 - 12m^2 +48m -64

It can be written as

=>(m^3 -64) -(12 m^2 -48m)

=>(m^3 - 4^3)-12m(m-4)

we know that a^3-b^3=(a-b)(a^2+ab+b^2)

=>(m-4)(m^2+4m+16)-12m(m-4)

=>(m-4)(m^2+4m+16-12m)

=>(m-4)(m^2-8m+16)

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

=>(m-4)(m-4)^2

=>(m-4)(m-4)(m-4)

(or)

Given expression is m^3-12m^2+48m-64

=>It can be written as

(m)^3-3(m)^2(4)+3(m)(4)^2-(4)^3

It is in the form of a^3-3a^2b+3ab^2-b^3

we know that

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

=>(m-4)^3

=>(m-4)(m-4)(m-4)

Answer:-

m^3 - 12m^2 +48m -64 = (m-4)(m-4)(m-4)

Used formulae:-

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