# What is the completely factored form of x^{4}y - 4x^{2}y - 5y?

**Solution:**

The factored form of the given expression x^{4}y - 4x^{2}y - 5y is worked out as follows:

x^{4}y - 4x^{2}y - 5y

= x^{4}y - 5x^{2}y + x^{2}y - 5y

= x^{2}y(x^{2} - 5) + y(x^{2} - 5)

= (x^{2} - 5)(x^{2}y + y)

= y(x^{2} + 1)(x^{2} - 5)

= y(x^{2} + 1)(x + √5)(x - √5)

Another example of factorization can be: Factorize x^{3} - x^{2} + ax + x - a - 1

Grouping the variables we have

x^{3} - x^{2} + ax - a + x - 1

x^{2}(x - 1) + a(x - 1) + 1(x -1)

(x - 1)(x^{2} + a + 1)

## What is the completely factored form of x^{4}y - 4x^{2}y - 5y?

**Summary:**

The completely factored form of x^{4}y - 4x^{2}y - 5y is y(x^{2} + 1)(x + √5)(x - √5).

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