### Chapter 3 - Algebra Coach Exercises

Algebra Coach Exercise on evaluating expressions.
Evaluate the following expressions, assuming that a = 1, b = 2, and c = 3. To do this drag-and-drop each expression into the Algebra Coach and then click the Evaluate button. Then type the values for a, b and c into the dialog box.
1. a + b + c
2. (a + 10 b + 100 c) / 5
3. sqrt (b^4 + c^2)

Algebra Coach Exercise on making substitutions.
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.
1. A = 3 x + y,   6 / (5 - A)
2. A = 3 x + y,   sqrt (A)
3. A = 3 x + y,   B = x - 2 y,   A / B
4. A = 3 x + y,   B = x - 2 y,   A ^ B

Algebra Coach Exercise on adding and subtracting expressions.
For each problem, expressions for A and B are given. Perform the indicated operation, either addition, A + B, or subtraction, AB. To do this drag-and-drop each problem into the Algebra Coach, then click on the Substitute button, then the Simplify button.
1. A = 2 x - y, B = 5 x - 3 y, A + B
2. A = 2 x - y, B = 5 x - 3 y, A - B
3. A = 2 x / 3, B = - 4 x / 3 + 9 y, A + B
4. A = 2 x / 3, B = - 4 x / 3 + 9 y, A - B
5. A = 2 m + 3 n, B = 2 m - 3 n, A + B
6. A = 2 m + 3 n, B = 2 m - 3 n, A - B
Simplify each of the following expressions. To do this drag-and-drop each expression into the Algebra Coach and then click the Simplify button.
1. 2 x - 5 x + y
2. 2 x / 3 - 4 x / 3 + 9 y
3. -(5 x - 10)
4. (2 a + 3 b + 4) - (2 a - 3 b)
5. (2 a + 3 b + 4) + (2 a - 3 b)
6. (5 a - b) + (2 a - b) - (7 a - 2 b)

Algebra Coach Exercise on integer exponents.
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:
1. x^3 * x^5
2. x^n / x^2
3. 3 a / (a^2 * a^3 * a^4)
4. (2 a b^2 c) ^ 4
5. (2 x ^ (-3)) ^ 2
6. (a / b^2) ^ 3
7. (-5 / b) ^ 3
8. (-2 a b /c) ^ 0
Simplify each of the following expressions. Express your answer without fractions, by using negative exponents. To do this drag-and-drop each expression into the Algebra Coach and click the Simplify button repeatedly.

Required Options settings: the negative exponent option must be set as shown here:
1. -6 / x^7
2. 3 a / (a^2 * a^3 * a^4)
3. (2 x ^ (-3)) ^ 2
4. (a / b^2) ^ 3
5. (-5 / b) ^ 3
After doing this exercise set the negative exponent option back to the default, show as fraction setting, shown here:

Algebra Coach Exercise on multiplying monomials.
For each problem, expressions for A and B are given. Multiply A · B. To do this drag-and-drop each problem into the Algebra Coach, then click on the Substitute button, then the Simplify button.
1. A = 2 x y, B = - 3 x z, A B
2. A = - 5 m n, B = - 4 m^2 n q, A B
3. A = -5, B = 2.2 y, A B
4. A = - a b, B = (b c)(c g), A B
For each question multiply the monomials. To do this drag-and-drop each question into the Algebra Coach and then click the Simplify button repeatedly.
1. (2 x y) (-3 x z)
2. (-5 a b) (-4 a^2 b c)
3. -5 (2.2 y)
4. -(a b) (b c) (c g)
5. (a x^m) (b x^n)

Algebra Coach Exercise on multiplying a monomial by a multinomial.
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.
1. 3 b (2 b + 6)
2. -x^3 (-4 x^2 + x - 5)
3. 3 x y (2 x y^2 - 3 x^2 y + x y)
4. - a b (a + b + a^2 b^2)
5. - a b (x + y + z)

Algebra Coach Exercise on multiplying multinomials.
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.
1. (a + b) (c + d)
2. (a + 3 b) (a - 3 b)
3. (2 a + 3 b) (2 a - 5 b)
4. (2 a + 3 b) ^ 2
5. (2 a + 1) (2 x - 5 y + 3)
6. (x - 2) (x - 3) (x + 4)

Algebra Coach Exercise on dividing a monomial by a monomial.
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, show as fraction setting, shown here:
1. (2 x y) / (-3 x z)
2. (-5 a b) / (-4 a^2 b c)
3. -5 / (2.2 y)
4. -(a b) (b c) / (c d)
5. (a x^m) / (b x^n)

Algebra Coach Exercise on dividing a multinomial by a monomial.
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, show as fraction setting, shown here:
1. (a + b - c) / x
2. (x + y + z) / (- a b)
3. (2 b + 6) / (3 b)
4. (-4 x^2 + x - 5) / (-x^3)
5. (2 x y^2 - 3 x^2 y + 2 x y) / (x y)
6. (a + b + a^2 b^2) / (- a b)