Question

Factoring the expression 20a^3b^3 – 24a^5b^2 + 4a^3b^2 gives a new expression of the form

Ua^xb^y (Wa^2 + Vb+ z), where U > 0.

What is the value of U?

What is the value of W?

What is the value of V?

What is the value of Z?

What is the value of x?

What is the value of y?

Answer 1

The value of U = 4

The value of W = -6

The value of V = 5

The value of Z = 1

The value of x = 3

The value of y =2

Explanation:

Given:

20a³b³ – 24a⁵b² + 4a³b²

Solution:

Lets first factorize this expression:

20a³b³ – 24a⁵b² + 4a³b²

= −24a⁵b² + 20a³b³ +4a³b²

Taking 4a³b² common

= 4a³b² (−6a² + 5b + 1) ___ (1)

Now you can see this expression takes the form:

Ua^xb^y (Wa^2 + Vb+ z), where U > 0.

`Ua^(x)b^(y) (Wa^(2) + Vb + z)`

Now you can clearly see from (1)

The value of U is 4

The value of W is -6

The value of V is 5

The value of Z is 1

The value of x is 3

The value of y is 2

However if we take minus common from above equation:

20a³b³ – 24a⁵b² + 4a³b²

= −24a⁵b² + 20a³b³ +4a³b²

Taking 4a³b² common

= - 4a³b² (6a² - 5b - 1) ___ (1)

In this case the value of U is - 4, W is 6 , V is -5, Z is -1 , x is 3 and b is 2