Factor x^2-8

Problem

x2−8

Solution

1. Identify the expression as a difference of squares by recognizing that 8 can be written as a square.

2. Rewrite the constant term using a square root to fit the form a2−b2

8=(√(,8))2

3. Simplify the square root by factoring out the perfect square.

√(,8)=√(,4⋅2)=2√(,2)

4. Apply the formula for the difference of squares, a2−b2=(a−b)*(a+b) where a=x and b=2√(,2)

(x−2√(,2))*(x+2√(,2))

Final Answer

x2−8=(x−2√(,2))*(x+2√(,2))

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