1.make up 10 different algebraic expressions 5 of them will have a single variable & 5 will have multiple variables

2.identify the
- variables
- coefficients
- constants
3.pick values for your variables and tell my what your expressions is worth

1. Algebraic expressions with a single variable:

a) 3x + 2
b) 5x^2 - 4x + 7
c) 2x^3 + 6x - 5
d) 3/x + 4
e) 8 - 2x

2. Algebraic expressions with multiple variables:
a) 2xy + 3z
b) 4x^2y - 3xz + 7y^2
c) 2x^3yz + 5xy^2 - 2z^2
d) x/y + z
e) 4 - 2xy

3. Variables, coefficients, and constants:
a) Variables: x, y, z
Coefficients: 3, 2
Constants: 2

b) Variables: x, y
Coefficients: 5, -4, 7
Constants: None

c) Variables: x
Coefficients: 2, 6, -5
Constants: None

d) Variables: x
Coefficients: 3, 4
Constants: None

e) Variables: x
Coefficients: -2
Constants: 8

f) Variables: x, y, z
Coefficients: 2, 3
Constants: None

g) Variables: x, y, z
Coefficients: 4, -3, 7
Constants: None

h) Variables: x, y, z
Coefficients: 2, 5, -2
Constants: None

i) Variables: x, y, z
Coefficients: 1, 1
Constants: None

j) Variables: x, y
Coefficients: -2
Constants: 4

Assuming random values:
- For expression a), if x = 2, then the expression is worth 8.
- For expression b), if x = 3 and y = -1, then the expression is worth 37.
- For expression c), if x = 1, then the expression is worth 3.
- For expression d), if x = 5, then the expression is worth 8/5.
- For expression e), if x = -1, then the expression is worth 10.

Please note that these values are arbitrary and may vary based on the context of the problem.

1. Algebraic expressions with a single variable:

a) 3x + 5
b) 2x^2 - 4x
c) 7x + 2x^2
d) x^3 + 2x^2 - x
e) 4x + 8x^2 - 3x^3

2. Algebraic expressions with multiple variables:
a) 2xy + 3z
b) x^2y^3 - 2xyz
c) 2x^2 + 3y - 4z
d) (x+y)^2 - 2xy
e) x^2y^2z - 3xyz^2

3. Variable, coefficient, and constant identification:
a) Variables: x, z, xy; Coefficients: 3, 2, 2; Constants: 5, 3
b) Variables: x; Coefficients: 2, -4; Constants: 0
c) Variables: x, x^2; Coefficients: 7, 2; Constants: 0
d) Variables: x; Coefficients: 1, 2, -1; Constants: 0
e) Variables: x, x^2, x^3; Coefficients: 4, 8, -3; Constants: 0

4. Assigning values to variables:
Let's assume x = 2, y = 3, and z = 4.

- For the expressions with a single variable:
a) 3x + 5 = 3(2) + 5 = 11
b) 2x^2 - 4x = 2(2^2) - 4(2) = 4
c) 7x + 2x^2 = 7(2) + 2(2^2) = 22
d) x^3 + 2x^2 - x = 2^3 + 2(2^2) - 2 = 10
e) 4x + 8x^2 - 3x^3 = 4(2) + 8(2^2) - 3(2^3) = -8

- For the expressions with multiple variables:
a) 2xy + 3z = 2(2)(3) + 3(4) = 16
b) x^2y^3 - 2xyz = (2^2)(3^3) - 2(2)(3)(4) = 128
c) 2x^2 + 3y - 4z = 2(2^2) + 3(3) - 4(4) = 3
d) (x+y)^2 - 2xy = (2+3)^2 -2(2)(3) = 13
e) x^2y^2z - 3xyz^2 = (2^2)(3^2)(4) - 3(2)(3)(4^2) = -144

1. Algebraic Expressions with a Single Variable:

a) 3x + 7
b) 2x^2 - 5x + 3
c) 4x + 2/x
d) x^3 + 3x^2 + 2x + 1
e) (x + 2)(x - 3)

2. Algebraic Expressions with Multiple Variables:
a) 2xy - 3xz + 5yz
b) 4xyz + 2xy - xz + y
c) x^2 + 2xy + y^2 - 3xz
d) 3x^2y + 2xyz - xy^2 + 4z
e) x^2y^2z^2 - 2xyz + 5z^3

3. Variables, Coefficients, and Constants:
- Variables are the symbols used to represent unknown quantities in an equation or expression. In the given expressions, variables are represented by x, y, and z.
- Coefficients are the numbers multiplied by the variables. In the expressions, coefficients are all numerical values, such as 3, 4, or 2.
- Constants are fixed values in an equation or expression that do not change. In the given expressions, constants are represented by numbers without any variables, like 7 or 1.

Now, let's pick some random values for the variables and find the values of the expressions:

Let's say:
x = 2, y = 3, z = 4 (random values)

For the expressions with a single variable:
a) 3x + 7 = 3(2) + 7 = 6 + 7 = 13
b) 2x^2 - 5x + 3 = 2(2^2) - 5(2) + 3 = 2(4) - 10 + 3 = 8 - 10 + 3 = 1
c) 4x + 2/x = 4(2) + 2/2 = 8 + 1 = 9
d) x^3 + 3x^2 + 2x + 1 = 2^3 + 3(2^2) + 2(2) + 1 = 8 + 12 + 4 + 1 = 25
e) (x + 2)(x - 3) = (2 + 2)(2 - 3) = 4(-1) = -4

For the expressions with multiple variables:
a) 2xy - 3xz + 5yz = 2(2)(3) - 3(2)(4) + 5(3)(4) = 12 - 24 + 60 = 48
b) 4xyz + 2xy - xz + y = 4(2)(3)(4) + 2(2)(3) - 2(3)(4) + 3 = 96 + 12 - 24 + 3 = 87
c) x^2 + 2xy + y^2 - 3xz = 2^2 + 2(2)(3) + 3^2 - 3(2)(4) = 4 + 12 + 9 - 24 = 1
d) 3x^2y + 2xyz - xy^2 + 4z = 3(2^2)(3) + 2(2)(3)(4) - 2(3)^2 + 4(4) = 36 + 144 - 18 + 16 = 178
e) x^2y^2z^2 - 2xyz + 5z^3 = 2^2(3)^2(4)^2 - 2(2)(3)(4) + 5(4)^3 = 576 - 48 + 320 = 848

Please note that the values provided for x, y, and z are arbitrary and can be replaced with any values to find the corresponding expression values.