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Factoring the expression 24a ^ 3b ^ 3 - 20a ^ 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 What is the value of x? What is the value of y?



Answer :

The values of the missing letters are; U = 4; W = -20; V = 6; Z = 1; x = 3; y = 2

How to factor Algebraic Expressions?

We are given the algebraic expression as;

24a³b³ - 20a⁵b² + 4a³b²

We want to express the given algebraic expression in the form:

U(a^x)(b^y)(Wa² + Vb+ z), where U > 0.

First of all, let us check the maximum common powers of a, b in each term from the given expression.

The maximum common power of a is 3 and

The maximum common power of b is 2.

So, we can take a³b² common out of each term.

And maximum common coefficient that can be taken out common is 4.

Taking 4 common from each term of given expression, we get:

4a³b²(6b - 20a² + 1)

Since we want to express as U(a^x)(b^y)(Wa² + Vb+ z), then we can say that; 4a³b²(-20a² + 6b + 1)

Thus;

U = 4

W = -20

V = 6

Z = 1

x = 3

y = 2

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