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Question

Accepted Answer

Step 1: Factorize the numerator 25a^2 - 10ab - 48b^2.

We look for two numbers whose product is (25)(-48) = -1200 and sum is -10.

These numbers are 30 and -40 because 30 × (-40) = -1200 and 30 + (-40) = -10.

Rewrite the middle term:
25a^2 + 30ab - 40ab - 48b^2

Group terms:
(25a^2 + 30ab) - (40ab + 48b^2)

Factor each group:
5a(5a + 6b) - 8b(5a + 6b)

Factor out common binomial:
(5a + 6b)(5a - 8b)

Step 2: Substitute back into the expression:
[(5a + 6b)(5a - 8b)] / (5a + 6b) × (5a + 8b)

Cancel (5a + 6b) from numerator and denominator:
(5a - 8b)(5a + 8b)

Step 3: Multiply the remaining binomials:
(5a)^2 - (8b)^2 = 25a^2 - 64b^2

Therefore, the simplified expression is 25a^2 - 64b^2.

Answer

Answer

Answer