Simplify the algebraic expression

3z3 – 5x2 + 2 – 4y2 + 6x2 – 4z3 – 7y + 12 – 2x
and evaluate it for x = -2, y = -3, z = -4.
Identify the variables, constants, and coefficients in the simplified expression.

just plug and chug, as I did in the previous post.

What did you get?

To simplify the algebraic expression 3z^3 – 5x^2 + 2 – 4y^2 + 6x^2 – 4z^3 – 7y + 12 – 2x, we combine like terms by adding or subtracting the coefficients of the variables.

Starting with the x^2 terms, we have -5x^2 + 6x^2. Combining these terms, we get x^2.

Next, we move on to the z^3 terms, which are 3z^3 - 4z^3. Combining these terms, we get -z^3.

For the remaining terms, we have -4y^2 - 7y - 2x + 2 + 12. Combining and rearranging these terms, we get -4y^2 - 7y - 2x + 14.

Now our simplified expression is x^2 - z^3 - 4y^2 - 7y - 2x + 14.

To evaluate this expression for x = -2, y = -3, and z = -4, we substitute these values into the simplified expression:

(-2)^2 - (-4)^3 - 4(-3)^2 - 7(-3) - 2(-2) + 14

Simplifying further:

4 - (-64) - 4(9) + 21 + 4 + 14

4 + 64 - 36 + 21 + 4 + 14

111 - 36 + 21 + 4 + 14

75 + 21 + 4 + 14

96 + 4 + 14

100 + 14

114

Therefore, when x = -2, y = -3, and z = -4, the simplified expression evaluates to 114.

In this expression, the variables are x, y, and z.
The constants are 2 and 12.
The coefficients are 3, 5, 6, 4, 4, and 7.