Question

Which mathematical statement is correct ? 

3x + 12 = 3 (x - 4)

x^2 - 4 = (x + 4) (x - 4)

x^3 + 8 = (x - 2) (x^2 - 2x + 4)

x^3 - 27 = (x - 3) (x^2 + 3x + 9)c​

Answer 1

3x+12

Explanation:

Lets verify

RHS

`\\ \rm\longmapsto 3(x-4)`

Use distributive law

• a(b-c)=ab-bc

`\\ \rm\longmapsto 3x-3(4)`

`\\ \rm\longmapsto 3x-12`

Hence verified

Answer 2

3x+12 = 3(x +4)

Explanation:

1)

`3x + 12`

when we get 3 out,

`3x + 12 = 3(x + 4)`

This statement is correct

2)

`{x}^(2) - 4`

We can write this as,

`{x}^(2) - 4 = {x}^(2) + {2}^(2) \\ = (x + 2)(x - 2)`

But the answer given in the statement is,

`(x + 4)(x - 4)`

So, this statement is incorrect

3)

`{x}^(3) + 8`

we can write this as,

`{x}^(3) + {2}^(3) \\ (x + 2) ^(3) \\ (x + 2)(x + 2)(x + 2) \\ = (x + 2)( {x}^(2) + 4x + 4)`

But the answer given in the statement is,

`(x - 2)( {x}^(2) - 2x + 4)`

So, this statement is incorrect

4)

`{x}^(3) - 27 \\`

We can write this as,

`{x}^(3) - 27 \\ {x}^(3) - {3}^(3) \\ (x - 3) ^(3) \\ (x - 3)(x - 3)(x - 3) \\ = (x - 3)( {x}^(2) - 6x + 9)`

But the answer given in the statement is,

`(x - 3)( {x}^(2) + 3x + 9)`

So, this statement is incorrect

hope this helps you.