The factorized expression using difference of squares is as follows,
9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)
Difference of Squares
Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares, a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.
Factorization Using Difference of Squares
Given expression is,
36a⁴b¹⁰ - 81a¹⁶b²⁰
= (6a²b⁵)² - (9a⁸b¹⁰)²
Using square of differences, we have
a² - b² = (a + b) (a - b)
Here, a = 6a²b⁵ and b = 9a⁸b¹⁰
Thus, we get,
(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)
Further Factorization
We can take out 3 common from both the bracket terms after applying difference of squares
3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)
= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)
Further, we can take out a²b⁵ as common from both the bracket terms
= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)
Learn more about difference of squares here:
https://brainly.com/question/11801811
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