Question

Simplify and determine the coefficient of (-x)(3y)(-2x). -4 1/3 1 4

Answer 1

The coefficient is 4.

(-2/3x)(3y)(-2x)

-2xy(-2x)

= 4x^2y

Answer 2

The coefficients are the constants -2/3, 3, and -2. You're supposed to multiply these together to get one term with one numerical constant which is the coefficient for the whole expression.

This is just a bunch of multiplications, (-2/3)*x*3*y*(-2)*x, and so the commutative law applies, which says that you can rearrange a multiplication any way you want. So put the numbers together, and the x's together and the y's together.

( (-2/3)*3*(-2) ) * (x^3 * x) * y

I'm also using the associative law, which says that I can put those parentheses in and multiply those groups of things together first. I'll bet you never thought "commutative law" and "associative law" were things that anybody actually used.

To simplify, multiply those things in the parentheses. x^3 * x is x^4. The product of those constants (-2/3), 3 and -2 is one number which is the coefficient. Source(s): Randy P · 8 years ago