[Aakash]

To factorize the expression (39y^3)(50y^2 – 98) ÷ (26y^2)(5y + 7), let’s break go step by step:

Step 1: Factorize the numerator (39y^3)(50y^2 – 98).

• We can find out a common factor of 2 from the expression to simplify it further:
  (39y^3)(50y^2 – 98) = 2(19y^3)(50y^2 – 98)

Step 2: Factorize the denominator (26y^2)(5y + 7).

• The expression (26y^2)(5y + 7) is already factored as much as possible, so leave it as it is.

Step 3: Divide the factored numerator by the factored denominator expression.

• Dividing (2(19y^3)(50y^2 – 98)) by ((26y^2)(5y + 7)) is equivalent to multiplying the numerator by the reciprocal of the denominator:
  (2(19y^3)(50y^2 – 98)) / ((26y^2)(5y + 7))

To simplify the expression further, let’s cancel out any common factors between the numerator and denominator. In this case, we can cancel out the common factors of 2 and y^2:

= (2(19y^3)(25y^2 – 49)) / ((13y^2)(5y + 7))

Now, the (2(19y^3)(25y^2 – 49)) / ((13y^2)(5y + 7)) is fully factored and simplified expression.