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How do you use the difference of two squares formula to factor #2x^2 − 18#?

Answer 1

You know that #a^2-b^2=(a+b)(a-b)# In your case #(2x^2-18)=(xsqrt(2)+sqrt(18))(xsqrt(2)-sqrt(18))=# #=(xsqrt(2)+sqrt(9*2))(xsqrt(2)-sqrt(9*2))=# #=(xsqrt(2)+3sqrt(2))(xsqrt(2)-3sqrt(2))=# #=sqrt(2)(x+3)sqrt(2)(x-3)=2(x+3)(x-3)#

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Answer 2

Savannah Anderson

To factor using integers, we may first remove the common factor of #2#. That will leave a difference of perfect squares.

#2x^2-18=2(x^2-9)=2(x^2-3^2)#

#=2(x+3)(x-3)#

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Answer 3

Eva Adamson

To factor (2x^2 - 18) using the difference of two squares formula, first factor out the greatest common factor, which is 2, to get (2(x^2 - 9)). Then, recognize that (x^2 - 9) is a difference of two squares, which factors further to ((x + 3)(x - 3)). So, the factored form of (2x^2 - 18) is (2(x + 3)(x - 3)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.