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mathlete13 eNotes educator| Certified Educator

To factor `4w^2-25`, it is helpful to observe that both terms are perfect squares. Because the two terms are being subtracted, this expression is an instance of the special factoring pattern called difference of squares, which factors as such:

`a^2-b^2=(a-b)(a+b)`

The values a and b are the square roots of the two terms. Therefore, in the given expression, a = 2w and b = 5. Thus, `4w^2-25` factors into (2w - 5)(2w + 5).