Chapter 7 Review (Gr. 8)

Monomials & Degrees

100

Are the following examples like monomials? xy and xy²

NO

200

What is the degree of the following expression? 17m⁵n¹¹

16

300

Are the following like monomials? 91x and 91y

NO

400

Find the degree of the expression. 4x⁹ - 2x⁶b⁶

12

500

Are the following like terms? 

a²b³c⁴d²ef⁴  and a²b³c⁴d²e¹f⁴

YES

e and e¹ = SAME

Simplify

100

3x²y + 2y³ - x²y + 2y³

2x²y + 4y³

200

-2a²b + 9ab² + 4a²b + 3ab

2a²b + 9ab² + 3ab

300

(9x² + 15x) - (12x² - 8x)

-3x² + 23x

9x² - 12x²  = -3x²

15x - (-8x) = +23x (flip sign)

400

(-2y³ + by² - 3z⁴) - (-4y³ + z⁴ - 2by²)

2y³ + 3by² - 4z⁴

-2y³ - (-4y³)  flip sign

+ by² - (- 2by²)  flip sign

- 3z⁴ - (z⁴)  add a negative

500

(8a - 3b + 4a² - 2b³ + c - 3c²)+(-2b + 2a² + 6c² - b³⁾  2c)

8a - 5b + 6a² - 3b³ + c + 3c²

8a + 0a = 8a, -3b -2b (flip signs = -5b)

4a² + 2a² = 6a² , -2b³ - b³ (flip sign = -3b³)

c + 0c = c

-3c² + 6c² = 3c²

Addition / Subtraction

100

(3x² + 5x) + (5x² + 2x)

8x² + 7x

200

(5g + 4h + 9gh) + (13h - 8gh - 6g)

-g + 17h + gh

300

(-2y³ + by² - 3z⁴) - (-4y³ + z⁴ - 2by²)

2y³ + 3by² - 4z⁴

-2y³ - (-4y³)  flip sign

+ by² - (- 2by²)  flip sign

- 3z⁴ - (z⁴)  add a negative

400

(3x³ - 2y⁴ + 3z³) + (-y⁴ - 2x³ -z³ + z¹²)

x³ - 3y⁴ + + z¹² + 2z³

500

(5a - 2b + 3c³ - 2b² + 4a³) - (-3a - 4b² + 2a³ + 6)

2a³ + 3c³ + 2b² + 8a - 2b  - 6 

5a - (-3a) = 8a (sign flip) ; -2b - 0 = -2b

3c³ - 0 = 3c³ ; -2b² - (-4b²) = 2b² (sign flip)

4a³ - 2a³ = 2a³ ; - (+6) = -6

Multiplication

100

(5x²z²)(3x²z²)

15x⁴z⁴

(3)(5)

x²⁺²

z²⁺²

200

-2ab³(3a³b - 2a²b² + ab³)

-6a⁴b⁴ + 4a³b⁵ - 2a²b⁶

-2ab³(3a³b) = 6a¹⁺³b³⁺¹

-2ab³(-2a²b²) = +4a¹⁺²b³⁺²

-2ab³( ab³) = -2a¹⁺¹b³⁺³

300

(6x - 1)(x + 6)

6x² + 35x -6

F: 6x(x) = 6x¹⁺¹

O: 6x(6) = 36x

I: -1(x) = -1x

L: -1(6) = -6

400

(2x + 5)(x+2)

2x² + 9x + 10

F: 2x(x)=2x²

O: 2x(2)=4x

I: 5(x) = 5x

L: 5(2) = 10

500

(y + 3)(y² + 3y + 9)

y³ + 6y² + 18y + 27

y(y²) + y(3y) + y(9) + 3(y²) + 3(3y) + 3(9)

y³ + 3y² + 9y + 3y² + 9y + 27

Division

100

30x⁶ ÷  6x²

5x⁴

30÷6 = 5

x^6-2 

200

9a⁴b³c ÷  a³b³

9ac

9÷1 = 9

a^4-3b^3-3c^1-0

300

-64x⁴y⁵z³  ÷  -8x⁴y²z¹

8y³z²

-64 ÷ -8 = +8

x^4-4 

y^5-2

z^3-1

400

(4x³ + 8x² - 6x) ÷ 2x

2x² + 4x - 3

4x³ ÷ 2x = 2x^3-1

8x² ÷ 2x = 2x^2-1

-6x ÷ 2x = -3x^1-1

500

(25x⁵ - 10x⁴ + 5x²) ÷  (5x² + 5x)

5x⁴ + 3x³ + x + 1

Group 1: 5x³ - 2x² + 1

Group 2: 5x⁴ - 2x³ + x

COMBINED: 5x⁴ + 5x³ - 2x³ + x + 1