You are given the expression 30x4y3 − 12x3y. PLEASE HURRY
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)
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Part B: I found the common factor by identifying the highest power of each variable present in both terms and taking the minimum of those powers along with the common numerical factor.
Part C:
\[ 30x^4y^3 - 12x^3y = 6x^3y(5x - 2) \]
Step-by-step explanation:
Part A: A common factor for the expression 30x^4y3 − 12x^3y is 6x^3y, because it is a factor that has a coefficient other than 1 and that contains at least one variable.
Part B: I found the common factor by looking at the coefficients and the variables of both terms. The coefficient of 30x^4y3 is 30 and the coefficient of -12x^3y is -12. The greatest common factor of 30 and -12 is 6. The variables of 30x^4y3 are x^4 and y^3 and the variables of -12x^3y are x^3 and y. The lowest power of each variable that appears in both terms is x^3 and y. Therefore, the common factor is 6x^3y.
Part C: To rewrite the expression using the common factor 6x^3y, we can divide both terms by 6x^3y and write the expression as a product of 6x^3y and the quotient. The quotient is obtained by dividing the coefficients and subtracting the powers of the variables. For example, 30x^4y3 / 6x^3y = (30 / 6) * (x^4 / x^3) * (y^3 / y) = 5 * x * y^2. Similarly, -12x^3y / 6x^3y = -2. Therefore, the expression rewritten using the common factor 6x^3y is:
30x^4y3 − 12x^3y = 6x^3y (5x * y^2 - 2)
I hope this helps you solve your problem. Have a nice day!