$$ {\displaylines x^4-5x^2+4\\ } $$ontbind in factoren$$  $$

We are tasked with factoring the following expression:

\[
x^4 - 5x^2 + 4
\]

To factor this, let's treat $x^4$ and $x^2$ terms as a quadratic in terms of $x^2$. Let's rewrite the expression by setting $y = x^2$. This gives us:

\[
y^2 - 5y + 4
\]

Now we factor this quadratic expression. We need two numbers that multiply to 4 and add to -5. These numbers are -4 and -1. So, we can factor it as:

\[
y^2 - 5y + 4 = (y - 4)(y - 1)
\]

Now, substitute back $y = x^2$, giving:

\[
(x^2 - 4)(x^2 - 1)
\]

Next, we factor both $x^2 - 4$ and $x^2 - 1$ as differences of squares:

\[
x^2 - 4 = (x - 2)(x + 2)
\]
\[
x^2 - 1 = (x - 1)(x + 1)
\]

Thus, the fully factored form of the expression is:

\[
(x - 2)(x + 2)(x - 1)(x + 1)
\]

### Final Answer:

\[
x^4 - 5x^2 + 4 = (x - 2)(x + 2)(x - 1)(x + 1)
\]

Would you like further clarification or more details? Here are some related questions for practice:

1. How would you factor $x^4 + 4x^2 + 3$?
2. Can you apply a similar technique to $x^4 - 9x^2 + 8$?
3. What is the difference of squares formula, and how does it help in factoring?
4. How do you factor expressions of the form $x^4 + 2x^2 - 8$?
5. How does recognizing patterns help simplify complex algebraic expressions?

**Tip:** When factoring higher-degree polynomials, try substituting variables to reduce the problem to a simpler quadratic equation!

$$ {\displaylines{x^4-5x^2+4\ }}$$ontbind in factoren$$

Learn how to factor the expression x^4 - 5x^2 + 4 by using substitution and the difference of squares formula. This problem explores key algebraic techniques, making it suitable for students in Grades 9-11.

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