factor using special product formulas

Question

Factor using special product formulas: b^(8)+a^(2)b^(4)+ 1/4 a^(4).

Answer 1

Mark was leading you in the right direction.

Let x = b^4 and y = a^2 / 2

Then, (x+y)^2 = x^2 + 2xy + y^2 = (b^4)^2 + 2 (b^4)(a^2 / 2) + (a^2 / 2)^2 =

b^8 + b^4 a^2 + a^4 / 4

Thus, we factor this as (b^4 + a^2 / 2) ^ 2

Answer 2

b⁸ + 2a²b⁴ + (1/4)a⁴

(b⁴)² + 2a²b⁴ + (1/4)(a²)²

 

This wold be a perfect square trinomial, with out the 1/4. Are you sure about it?