Simplify the algebraic expression
3xz + 4xy – 2yz + xy + 5yz – 9xz
and evaluate it for x = 3, y = -2, z = -5.
Identify the variables, constants, and coefficients in the simplified expression.
simplified (just a bit)
x(5y-6z) + 3yz
3(-10+30) + 3(-2)(-5) = 90
4xy+5yz-9xz-4xy
To simplify the algebraic expression 3xz + 4xy - 2yz + xy + 5yz - 9xz, we can combine like terms. Like terms are terms that have the same variables and exponents.
First, let's combine the terms that have both x and z variables:
3xz - 9xz = (3 - 9)xz = -6xz
Next, let's combine the terms that have both x and y variables:
4xy + xy = (4 + 1)xy = 5xy
Finally, let's combine the terms that have both y and z variables:
-2yz + 5yz = (-2 + 5)yz = 3yz
The simplified expression becomes:
-6xz + 5xy + 3yz
To evaluate this expression for x = 3, y = -2, and z = -5, we substitute the values into the expression:
-6(3)(-5) + 5(3)(-2) + 3(-2)(-5)
Simplifying this expression further:
90 + (-30) + 30 = 90 - 30 + 30 = 90
Therefore, when x = 3, y = -2, and z = -5, the simplified expression evaluates to 90.
Now let's identify the variables, constants, and coefficients in the simplified expression -6xz + 5xy + 3yz:
Variables: x, y, z
Constants: -6, 5, 3
Coefficients: -6, 5, 3
Note that the coefficients are the numerical values in front of the variables in each term.