Question

completely factor the given polynomial, if possible. if the polynomial cannot be factored, indicate
ot factorable\.

\\2y^2 - 8x^2\\

Explanation:

Identify the greatest common factor

Using the Factoring Polynomials by GCF knowledge point, we find the greatest common factor of the terms in the polynomial \(2y^2 - 8x^2\).
The greatest common factor of the coefficients \(2\) and \(-8\) is \(2\).
Factoring out \(2\) gives:

$$2(y^2 - 4x^2)$$

Apply the difference of squares formula

Using the Difference of Squares knowledge point, we factor the binomial inside the parentheses.
The expression \(y^2 - 4x^2\) is a difference of two perfect squares:

$$y^2 - 4x^2 = (y)^2 - (2x)^2$$

Applying the formula \(a^2 - b^2 = (a - b)(a + b)\):

$$y^2 - 4x^2 = (y - 2x)(y + 2x)$$

Write the completely factored polynomial

Combining the factored parts, we write the final completely factored expression:

$$2(y - 2x)(y + 2x)$$

Answer:

\(2(y - 2x)(y + 2x)\)