Question

The factor from of (a^4b^4-16c^4)is​

Answer 1

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Factor 16a^4-81b^4

16a4−81b416a4-81b4

Rewrite 16a416a4 as (4a2)2(4a2)2.

(4a2)2−81b4(4a2)2-81b4

Rewrite 81b481b4 as (9b2)2(9b2)2.

(4a2)2−(9b2)2(4a2)2-(9b2)2

Since both terms are perfect squares, factor using the difference of squares formula, a2−b2=(a+b)(a−b)a2-b2=(a+b)(a-b) where a=4a2a=4a2and b=9b2b=9b2.

(4a2+9b2)(4a2−(9b2))(4a2+9b2)(4a2-(9b2))

Simplify.

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(4a2+9b2)(2a+3b)(2a−3b)(4a2+9b2)(2a+3b)(2a-3b)

16a4−81b416a4-81b4

81b381b3

8ab