Q. 274 - Intermediate Algebra

Question

The difference of squares, $y^4-625$ can be factored as, $\left(y^2-25\right)\left(y^2+25\right)$. But it is not completely factored. What more must be done to completely factor.

Step-by-Step Solution

Answer

We need to use the difference and sum of squares formula to factor further and solve the equation

Step 1: Given information

Given the polynomial, $y^4-625$

Step 2: Factorise further

On factorising, we get

$$\begin{gathered} y^4-625=0 \\ (y^2-25)(y^2+25)=0 \\ (y-5)(y+5)(y^2+25)=0 \\ y=5,-5 \end{gathered}$$ since square can't be negative