Questions: 2y^2-8x^2

Transcript text: 2y^{2}-8x^{2}

Solution

Solution Steps

The given expression \(2y^2 - 8x^2\) can be simplified by factoring out the greatest common factor. In this case, the greatest common factor is 2. After factoring out 2, we can check if the remaining expression is a difference of squares.

Step 1: Rewrite the Expression

The original expression is given as: \[ 2y^2 - 8x^2 \]

Step 2: Factor Out the Greatest Common Factor

We can factor out the greatest common factor, which is \(2\): \[ 2(y^2 - 4x^2) \]

Step 3: Recognize the Difference of Squares

The expression \(y^2 - 4x^2\) is a difference of squares, which can be factored further: \[ y^2 - (2x)^2 = (y - 2x)(y + 2x) \]

Step 4: Combine the Factors

Combining the factors, we have: \[ 2(y - 2x)(y + 2x) \]

Final Answer

Thus, the completely factored form of the expression \(2y^2 - 8x^2\) is: \[ \boxed{2(y - 2x)(y + 2x)} \]

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