Question

Factor the binomial 64-a^4b^4

Answer 1

The binomial 64 - a^4b^4 can be factored by recognizing it as a difference of squares, resulting in (8 + a^2b^2)(8 - a^2b^2).

Step-by-step explanation:

To factor the binomial 64 - a4b4, we can recognize it as a difference of squares. The difference of squares formula is (x2 - y2) = (x + y)(x - y). In this case, 64 can be written as (8)2 and a4b4 can be written as (a2b2)2. Applying the difference of squares formula, we have:

• First, express both terms as squares: 64 = 82 and a4b4 = (a2b2)2.
• Then apply the difference of squares: 64 - a4b4 = (8)2 - (a2b2)2.
• Factor as (8 + a2b2)(8 - a2b2).

So, the binomial 64 - a4b4 factors to (8 + a2b2)(8 - a2b2).