Final answer:
To expand the expression, use the FOIL method and combine like terms. The simplified expression is 16/25 a^2 - 25b^2.
Step-by-step explanation:
To expand the expression, you can use the FOIL method. FOIL stands for First, Outer, Inner, Last. Multiply the first terms of each binomial, then multiply the outer terms, then multiply the inner terms, and finally multiply the last terms. Combine like terms to simplify the expression.
In this case, the expression is (4/5 a + 5b)(4/5 a - 5b). Applying the FOIL method, we get: (4/5 a * 4/5 a) + (4/5 a * -5b) + (5b * 4/5 a) + (5b * -5b).
Simplifying each term and combining like terms, we have: (16/25 a^2) - (20/5 a * b) + (20/5 a * b) - (25b^2) = 16/25 a^2 - 25b^2.