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You are given the expression 30x4y3 − 12x3y.

Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable.

Part B: Explain how you found the common factor.

Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work.

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Step-by-step explanation:

Answer:

The common factor is 6x^3y and the equivalent expression is 6x^3y(5x - 2)

Part A: Find a common factor for the expression

The expression is given as:

30x^4y^3 - 12x^3y

Factorize each term of the expression

So, we have

30x^4y^3 = 2 * 3 * 5 * x * x * x * x * y * y * y

12x^3y = 2 * 2 * 3 * x * x * x * y

Multiply the common factors

So, we have

Common factor = 2 * 3 * x * x * x * y

This gives

Common factor = 6x^3y

Hence, the common factor is 6x^3y

Part B: Explain how you found the common factor

See part A for explanation

Part C: Rewrite the expression using the common factor you found in Part A.

In (a), we have:

30x^4y^3 - 12x^3y

Common factor = 6x^3y

Divide each term by the common factor

So, we have

6x^3y(5x - 2)

Hence, the equivalent expression is 6x^3y(5x - 2)

Step-by-step explanation:

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