Factor by making it a perfect square

Question

Solve this by factoring it by making it a perfect square

x^4+15x^2+64

Answer 1

use the difference of square formula

a²-b²=(a+b)(a-b) where a=x²+8 and b=x

x^4+15x^2+64=(x²+x+8)(x²-x+8)

Answer 2

The trinomial would be a perfect square trinomial if the 15 was a 16. So, add a 1x² and subtract a 1x² to change the appearance of this algebraic expression to:

[x⁴ +16x²+64] - x² (confirm that this is equivalent to the original expression).

Now rewrite the trinomial (in the brackets) as a binomial squared.

[(x²+8)²] - x²

That expression is a difference of squares, so use the format: (a²- b²) = (a + b)(a - b)

where a = x²+8 and b = x.

Take it from there!