Question

The diagram represents a difference of squares.

What are the factors of m2 – 6m + 6m – 36?

a. (m – 2)(m + 18)
b. (m – 3)(m + 3)
c. (m – 4)(m + 9)
d. (m – 6)(m + 6)

Answer 1

The answer is d.

Step-by-step explanation:
To start with, classify the first two terms and factor out the common factor. i.e m is a common factor of m2-6m. By factoring it out we get m(m-6).

Follow the same procedure for terms three and four. ie
6 is a common factor of 6m-36. By factoring out, 6(m-6)
Regrouping
m(m-6)+6(m-6)
By factoring out (m-6), we get:
(m-6)(m+6)

Answer 2

Option D
`(m-6)(m+6)`

Step-by-step explanation:

we have

`m^(2) -6m+6m-36`

Simplify

`m^(2) -6m+6m-36=m^(2) -36`

we know that

In a difference of square

`(a^(2)-b^(2))=(a+b)(a-b)`

Remember that

`36=6^(2)`

therefore

`(m^(2)-6^(2))=(m+6)(m-6)`