Factor completely. 162p^2–242

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Identify GCF: Identify the greatest common factor (GCF) of the terms 162p^2 and 242. Both numbers are even, so 2 is a factor. We can check for higher factors that are common to both numbers.Divide by 2: Divide both 162 and 242 by 2 to see if there is a larger common factor. 162 ÷ 2 = 81 and 242 ÷ 2 = 121. Both 81 and 121 are perfect squares (9^2 and 11^2, respectively), so the GCF is not just 2. We can try to factor out a larger number.Check for 3: Since 81 and 121 are both multiples of 3, we can divide them by 3 to see if 3 is a common factor. 81 ÷ 3 = 27 and 121 is not divisible by 3. Therefore, 3 is not a common factor for both terms. We should go back and check for the largest common factor that includes 2.Factor out 2: We know that 81 is 3^4 and 121 is 11^2. Since 3 is not a factor of 121, we can conclude that the GCF is 2. Now we can factor out 2 from both terms.Factor inside parentheses: Factoring out the GCF of 2, we get 2(81p^2 - 121). We can now look at each term inside the parentheses to see if they can be factored further.Apply difference of squares: Inside the parentheses, we have a difference of squares since 81p^2 is (9p)^2 and 121 is 11^2. We can factor the difference of squares as (a^2 - b^2) = (a + b)(a - b).Verify factoring: Apply the difference of squares factoring to get 2((9p + 11)(9p - 11)).Check the factoring for any possible errors. 2 * (9p + 11) * (9p - 11) should expand back to the original expression 162p^2 - 242. Let's expand it to verify: 2 * (81p^2 - 99p + 99p - 121) simplifies to 2 * (81p^2 - 121), which is 162p^2 - 242. The factoring is correct.

Factor completely. $162p^2-242$

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Factor completely. $162p^2-242$