Simplify using Factorization: (65y^3(50y^2-98))/(26y^2(5y+7))

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Write Expression: Write down the expression that needs to be simplified. 65y^3(50y^2 - 98) / 26y^2(5y + 7)Factor Common Factors: Factor out the common factors in the numerator and the denominator. In the numerator, 65y^3 is a common factor, and in the denominator, 26y^2 is a common factor. We can also notice that 65 = 13 * 5 and 26 = 13 * 2, so there is a common factor of 13 in the numerator and denominator.Simplify Common Factors: Simplify the common factors between the numerator and the denominator. Divide both the numerator and the denominator by the common factors. We have: 65 / 26 = 5 / 2 (since both are divisible by 13) y^3 / y^2 = y (since y^3 divided by y^2 is y) Now the expression looks like this: (5/2) * y * (50y^2 - 98) / (5y + 7)Find Common Factors: Look for common factors in the remaining terms of the numerator and the denominator. We can factor the numerator 50y^2 - 98 by looking for a common factor of 50 and 98, which is 2. So we can write: 50y^2 - 98 = 2(25y^2 - 49) Notice that 25y^2 - 49 is a difference of squares and can be factored further as (5y + 7)(5y - 7).Rewrite with Factored Form: Rewrite the expression with the factored form of the numerator. Now the expression is: (5/2) * y * 2(5y + 7)(5y - 7) / (5y + 7)Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. The (5y + 7) term is present in both the numerator and the denominator, so they cancel each other out. We are left with: (5/2) * y * 2 * (5y - 7)Simplify Remaining Expression: Simplify the remaining expression. The 2 in the numerator and the 2 in the denominator cancel each other out, leaving us with: 5y * (5y - 7)Multiply Remaining Terms: Multiply out the remaining terms. 5y * (5y - 7) = 25y^2 - 35y

Simplify using Factorization: $(65y^3(50y^2-98))/(26y^2(5y+7))$

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Simplify using Factorization: (65y3(50y2−98))/(26y2(5y+7))(65y^3(50y^2-98))/(26y^2(5y+7))(65y3(50y2−98))/(26y2(5y+7))

Simplify using Factorization: $(65y^3(50y^2-98))/(26y^2(5y+7))$