What is the completely factored form of x⁴y - 4x²y - 5y?

Solution:

The factored form of the given expression x⁴y - 4x²y - 5y is worked out as follows:

x⁴y - 4x²y - 5y

= x⁴y - 5x²y + x²y - 5y

= x²y(x² - 5) + y(x² - 5)

= (x² - 5)(x²y + y)

= y(x² + 1)(x² - 5)

= y(x² + 1)(x + √5)(x - √5)

Another example of factorization can be: Factorize x³ - x² + ax + x - a - 1

Grouping the variables we have

x³ - x² + ax - a + x - 1

x²(x - 1) + a(x - 1) + 1(x -1)

(x - 1)(x² + a + 1)

What is the completely factored form of x⁴y - 4x²y - 5y?

Summary:

The completely factored form of x⁴y - 4x²y - 5y is y(x² + 1)(x + √5)(x - √5).