What is the completely factored form of 2x2 – 32? a.(2x2 + 16)(x – 16) b.2(x + 4)(x – 4) c.2(x + 8)(x – 4) d.2(x – 8)(x – 4)

Firstly, we can see that 2 goes into both terms of the expression, so we can factor it out like so: 2(x^2 - 16). Now we can spot a difference of two squares expression, as we have an x^2 minus a square number. Remember that the difference of two squares is in the format: (x+a) (x-a), and when expanded, gives you x^2-a^2. Using this information we square root 16 to find out the a value, so a=4. Therefore, your answer is B. 2(x+4)(x-4)

2(x+4)(x-4)

Explanation:
Before we begin, remember the rule of the difference between squares which is as follows:
a² - b² = (a-b)(a+b)

Now, for the given:
2x² - 32
Take 2 as a common factor:
2(x²-16)
This can be rewritten as:
2(x²-(4)²))
Now, factorize using the difference between squares mentioned above:
2(x+4)(x-4)
This would be the simplest form that could be reached for this expresion

Hope this helps :)

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