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Factor completely. $98r^2-50$

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Factor polynomials

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Q. Factor completely.

98r^2-50

Identify GCF: Identify the greatest common factor (GCF) of the terms $98r^2$ and $50$ . The GCF of $98$ and $50$ is $2$ .
Divide and Find: Divide each term by the GCF to find what will be inside the parentheses after factoring. $\newline$ $98r^2 \div 2 = 49r^2$ $\newline$ $50 \div 2 = 25$
Write Product: Write the expression as the product of the GCF and the factored terms. $\newline$ $2(49r^2 - 25)$
Recognize Perfect Squares: Recognize that $49r^2$ and $25$ are both perfect squares. $49r^2$ is the square of $7r$ , and $25$ is the square of $5$ .
Apply Difference of Squares: Since we have a difference of squares, we can factor it as $(a^2 - b^2) = (a + b)(a - b)$ . In this case, $a = 7r$ and $b = 5$ .
Write Final Form: Write the final factored form using the difference of squares formula. $\newline$ $2(7r + 5)(7r - 5)$

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