Simplify using Factorization: (39y^3(50y^2-98))/(52y^2(5y+7))

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Factor Common Factors: Factor out the common factors in the numerator and the denominator. The numerator is 39y^3(50y^2-98) and the denominator is 52y^2(5y+7). We can see that both the numerator and the denominator have common factors of y^2 and numbers that are multiples of 13.Factor by Greatest Divisor: Factor 39 and 52 by their greatest common divisor, which is 13. 39 = 13 * 3 52 = 13 * 4 Now we can rewrite the expression with these factors. (13 * 3 * y^3 * (50y^2 - 98)) / (13 * 4 * y^2 * (5y + 7))Cancel Common Factors: Cancel out the common factors. The common factors of 13 and y^2 can be canceled from the numerator and the denominator. This leaves us with: (3 * y * (50y^2 - 98)) / (4 * (5y + 7))Factor Expression: Factor the expression 50y^2 - 98 by looking for a common factor. Both terms are divisible by 2. 50y^2 - 98 = 2 * (25y^2 - 49) Now we can rewrite the expression with this factor. (3 * y * 2 * (25y^2 - 49)) / (4 * (5y + 7))Factor Difference of Squares: Notice that 25y^2 - 49 is a difference of squares and can be factored further. 25y^2 - 49 = (5y)^2 - 7^2 = (5y + 7)(5y - 7) Now we can rewrite the expression with this factor. (3 * y * 2 * (5y + 7)(5y - 7)) / (4 * (5y + 7))Cancel Common Factor: Cancel out the common factor of (5y + 7) from the numerator and the denominator. This leaves us with: (3 * y * 2 * (5y - 7)) / 4Simplify Coefficients: Simplify the remaining expression by dividing the coefficients. 3 * 2 = 6 6 / 4 = 3 / 2 Now we have: (3/2) * y * (5y - 7)Distribute (3/2): Distribute the (3/2) across the terms in the parentheses. (3/2) * y * 5y = (15/2) * y^2 (3/2) * y * (-7) = (-21/2) * y The simplified expression is: (15/2) * y^2 - (21/2) * y

Simplify using Factorization: $(39y^3(50y^2-98))/(52y^2(5y+7))$

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Simplify using Factorization: (39y3(50y2−98))/(52y2(5y+7))(39y^3(50y^2-98))/(52y^2(5y+7))(39y3(50y2−98))/(52y2(5y+7))

Simplify using Factorization: $(39y^3(50y^2-98))/(52y^2(5y+7))$