Question

You are given the expression 36x4y3 − 16x3y. Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point) Part B: Explain how you found the common factor. (1 point) Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)

Answer 1

The expression can be rewritten as 4x³y. (9x - 4).

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

The given expression is
`36x^4y^3 4y^3 - 16x^3y.`

A common factor for the expression that has a coefficient other than 1 and contains at least one variable is 4x³y.

Part B: Explain how you found the common factor.

To find the common factor, identify the smallest exponent for each variable that appears in both terms. In this case, the common factor is 4x³y, 3 as it is the smallest combination of the coefficients (4 and 1) and the variables (x^3 and y) that appears in both terms.

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

The given expression is
`36x^4y^3 - 16x3y.`

Step 1: Identify the common factor 4x3y. 3 (9x-4)

So, the expression can be rewritten as 4x³y. (9x - 4).