Evaluate the following expressions, assuming that

- a + b + c
- (a + 10 b + 100 c) / 5
- sqrt (b^4 + c^2)

Drag-and-drop each of these problems into the Algebra Coach and then click the Substitute button. This replaces all the literals (letters) in the last expression by the quantities given in the previous expressions.

- A = 3 x + y, 6 / (5 - A)
- A = 3 x + y, sqrt (A)
- A = 3 x + y, B = x - 2 y, A / B
- A = 3 x + y, B = x - 2 y, A ^ B

For each problem, expressions for

- A = 2 x - y, B = 5 x - 3 y, A + B
- A = 2 x - y, B = 5 x - 3 y, A - B
- A = 2 x / 3, B = - 4 x / 3 + 9 y, A + B
- A = 2 x / 3, B = - 4 x / 3 + 9 y, A - B
- A = 2 m + 3 n, B = 2 m - 3 n, A + B
- A = 2 m + 3 n, B = 2 m - 3 n, A - B

- 2 x - 5 x + y
- 2 x / 3 - 4 x / 3 + 9 y
- -(5 x - 10)
- (2 a + 3 b + 4) - (2 a - 3 b)
- (2 a + 3 b + 4) + (2 a - 3 b)
- (5 a - b) + (2 a - b) - (7 a - 2 b)

Simplify each expression. Express your answer without negative exponents, by using fractions. To do this drag-and-drop each expression into the Algebra Coach and then click the Simplify button repeatedly.

Required Options settings: the negative exponent option must be set as shown here:

- x^3 * x^5
- x^n / x^2
- 3 a / (a^2 * a^3 * a^4)
- (2 a b^2 c) ^ 4
- (2 x ^ (-3)) ^ 2
- (a / b^2) ^ 3
- (-5 / b) ^ 3
- (-2 a b /c) ^ 0

Required Options settings: the negative exponent option must be set as shown here:

- -6 / x^7
- 3 a / (a^2 * a^3 * a^4)
- (2 x ^ (-3)) ^ 2
- (a / b^2) ^ 3
- (-5 / b) ^ 3

For each problem, expressions for

- A = 2 x y, B = - 3 x z, A B
- A = - 5 m n, B = - 4 m^2 n q, A B
- A = -5, B = 2.2 y, A B
- A = - a b, B = (b c)(c g), A B

- (2 x y) (-3 x z)
- (-5 a b) (-4 a^2 b c)
- -5 (2.2 y)
- -(a b) (b c) (c g)
- (a x^m) (b x^n)

For each question multiply the monomial by the multinomial. To do this drag-and-drop each question into the Algebra Coach and then click the Distribute button.

- 3 b (2 b + 6)
- -x^3 (-4 x^2 + x - 5)
- 3 x y (2 x y^2 - 3 x^2 y + x y)
- - a b (a + b + a^2 b^2)
- - a b (x + y + z)

For each question multiply the multinomials. To do this drag-and-drop each question into the Algebra Coach and then click the Distribute button repeatedly.

- (a + b) (c + d)
- (a + 3 b) (a - 3 b)
- (2 a + 3 b) (2 a - 5 b)
- (2 a + 3 b) ^ 2
- (2 a + 1) (2 x - 5 y + 3)
- (x - 2) (x - 3) (x + 4)

For each question divide the monomials. To do this drag-and-drop each question into the Algebra Coach and then click the Simplify button repeatedly.

Required options setting: the negative exponent option should be set to the default,

- (2 x y) / (-3 x z)
- (-5 a b) / (-4 a^2 b c)
- -5 / (2.2 y)
- -(a b) (b c) / (c d)
- (a x^m) / (b x^n)

For each question divide the monomial into each term of the multinomial. To do this drag-and-drop each question into the Algebra Coach and then click the Distribute button.

Required options setting: the negative exponent option should be set to the default,

- (a + b - c) / x
- (x + y + z) / (- a b)
- (2 b + 6) / (3 b)
- (-4 x^2 + x - 5) / (-x^3)
- (2 x y^2 - 3 x^2 y + 2 x y) / (x y)
- (a + b + a^2 b^2) / (- a b)