How do you use the difference of two squares formula to factor 2x^2 − 182x2−18?

2 Answers
Gió
May 6, 2015

You know that a^2-b^2=(a+b)(a-b)a2−b2=(a+b)(a−b)
In your case
(2x^2-18)=(xsqrt(2)+sqrt(18))(xsqrt(2)-sqrt(18))=(2x2−18)=(x√2+√18)(x√2−√18)=
=(xsqrt(2)+sqrt(9*2))(xsqrt(2)-sqrt(9*2))==(x√2+√9⋅2)(x√2−√9⋅2)=
=(xsqrt(2)+3sqrt(2))(xsqrt(2)-3sqrt(2))==(x√2+3√2)(x√2−3√2)=
=sqrt(2)(x+3)sqrt(2)(x-3)=2(x+3)(x-3)=√2(x+3)√2(x−3)=2(x+3)(x−3)

Jim H
May 6, 2015

To factor using integers, we may first remove the common factor of 22. That will leave a difference of perfect squares.

2x^2-18=2(x^2-9)=2(x^2-3^2)2x2−18=2(x2−9)=2(x2−32)

=2(x+3)(x-3)=2(x+3)(x−3)

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