Expanding and Simplifying the Expression (5x+3)(5x3)(2x5)^2
This article will guide you through the process of expanding and simplifying the algebraic expression: (5x+3)(5x3)(2x5)^2.
Expanding the Expressions
Let's break down the expression into its components:

(5x+3)(5x3): This is a product of two binomials in the form (a+b)(ab). We can use the difference of squares pattern to expand it:
 (a+b)(ab) = a^2  b^2
 Therefore, (5x+3)(5x3) = (5x)^2  (3)^2 = 25x^2  9

(2x5)^2: This is a square of a binomial. We can use the square of a binomial pattern to expand it:
 (ab)^2 = a^2  2ab + b^2
 Therefore, (2x5)^2 = (2x)^2  2(2x)(5) + (5)^2 = 4x^2  20x + 25
Combining the Expanded Terms
Now, we can substitute the expanded forms back into the original expression:
(5x+3)(5x3)(2x5)^2 = (25x^2  9)  (4x^2  20x + 25)
Finally, we can simplify the expression by combining like terms:
25x^2  9  4x^2 + 20x  25 = 21x^2 + 20x  34
Conclusion
Therefore, the simplified form of the expression (5x+3)(5x3)(2x5)^2 is 21x^2 + 20x  34.