To factor the expression [tex]\(64x^2 - 25y^2\)[/tex], we recognize that it is a difference of squares. The difference of squares formula states:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
For the given expression, [tex]\(64x^2\)[/tex] and [tex]\(25y^2\)[/tex] can each be written as squares:
[tex]\[
64x^2 = (8x)^2 \quad \text{and} \quad 25y^2 = (5y)^2
\][/tex]
Thus, the given expression can be rewritten as:
[tex]\[
64x^2 - 25y^2 = (8x)^2 - (5y)^2
\][/tex]
Applying the difference of squares formula, where [tex]\(a = 8x\)[/tex] and [tex]\(b = 5y\)[/tex], we get:
[tex]\[
(8x)^2 - (5y)^2 = (8x - 5y)(8x + 5y)
\][/tex]
So, the factored form of the expression [tex]\(64x^2 - 25y^2\)[/tex] is:
[tex]\[
(8x - 5y)(8x + 5y)
\][/tex]
Therefore, the answer is:
[tex]\[
(8x - 5y)(8x + 5y)
\][/tex]
