Respuesta :

iiMGii
Let's solve this problem step-by-step.

First of all, let's establish that we are trying to obtain the factorised expression for:

2x^2 + 18

Now, there are two main ways we can solve this problem:

1 ) Expand and then simplify each of the options until one of them gives you the correct answer.

OR

2 ) Factorise the expression to give you one of the options as your answer.

I will be doing the first method today as although it is more time-consuming, it is easier to do as if you aren't able to directly factorise the expression you can use your expanding skills instead.

STEP-BY-STEP SOLUTION:

To begin with, we will expand and simplify each of the expressions to see which one gives us the correct answer as displayed below:

OPTION A -
= ( 2x - 9 ) ( x - 2 )
= 2x^2 - 4x - 9x + 18
= 2x^2 - 15x + 18
Therefore, Option A is incorrect.

OPTION B -
= ( 2x - 6 ) ( x - 3 )
= 2x^2 - 6x - 6x + 18
= 2x^2 - 12x + 18
Therefore, Option B is incorrect.

OPTION C -
= ( 2x - 6 ) ( x + 3 )
= 2x^2 + 6x - 6x - 18
= 2x^2 - 18
Therefore, Option C is incorrect.

OPTION D -
= ( 2x - 9 ) ( x + 2 )
= 2x^2 + 4x - 9x - 18
= 2x^2 - 5x - 18
Therefore, Option D is incorrect.

Hmmm, this is weird. I think that there is a mistake in either the question or answer options as all the options ended up being incorrect.

However, I believe it would be safest to pick the closest answer which would be Option C.

ANSWER:
Option C - ( 2x - 6 ) ( x + 3 )

The expression [tex]2x^{2} +18[/tex] is equal to [tex](2x-6i)(x+3i)[/tex].

The correct answer is option C.

[tex]i^{2}=-1[/tex]

A. [tex](2x-9i)(x-2i)[/tex]

[tex]= 2x(x)-2x(2i)-9i(x)-9i(-2i)\\=2x^{2} -4xi-9xi-18\\=2x^{2} -13xi-18[/tex]

[tex]2x^{2} -13xi-18[/tex] ≠ [tex]2x^{2} +18[/tex]

B. [tex](2x-6i)(x-3i)[/tex]

[tex]=2x^{2}-6xi-6xi-18\\=2x^{2} -12xi-18[/tex]

[tex]2x^{2} -12xi-18[/tex] ≠ [tex]2x^{2} +18[/tex]

C. [tex](2x-6i)(x+3i)[/tex]

[tex]=2x^{2} +6xi-6xi+18\\=2x^{2} +18[/tex]

[tex]2x^{2} +18=2x^{2} +18[/tex]    [tex](LHS=RHS)[/tex]

Therefore, the expression [tex]2x^{2} +18[/tex] is equal to [tex](2x-6i)(x+3i)[/tex].

For more information:

ttps://brainly.com/question/23672426

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