Pre-Algebra Unit 2 Review

Translating Expressions

100

5 less than two-thirds a number

2/3 n - 5

200

the difference between a number squared and 6

n² - 6

300

the sum of -2 and twice a number

-2 + 2n

400

the quotient of a negative number and 10

-n/10

500

Translate and simplify:

Subtract 5p²q⁴ from -3p²q⁴.

-3p²q⁴ - 5p²q⁴ = -8p²q⁴

Simplifying Expressions

100

Distribute:

5(2x + 7)

10x + 35

200

Factor. Write "prime" if it cannot be factored.

24a + 36b

GCF = 12

12(2a + 3b)

300

-4x² + 3xy + 6x² + 7xy

2x² + 10xy

400

3(4x + 5) - 6x + 8

= 12x + 15 - 6x + 8

= 6x + 23

500

Simplify, then factor:

5(2x - 3) - 7x

= 10x - 15 - 7x

= 3x - 15

= 3(x - 5)

Exponent Rules

100

2⁵/2³

2²

200

(2x)(7x⁵)

14x⁶

300

(2y³)⁵

32y¹⁵

400

(3a³b⁶)² - 4a⁶b¹²

= 9a⁶b¹² - 4a⁶b¹²

= 5a⁶b¹²

500

(3x³y² - 5x³y²)²

= (-2x³y²)²

= 4x⁶y⁴

Operations with Scientific Notation

100

(1.3 x 10⁴) + (5.9 x 10⁴)

7.2 x 10⁴

200

(4 x 10^-2) - (1.2 x 10^-3)

= (4 x 10^-2) - (0.12 x 10^-2)

= 3.88 x 10^-2

300

(6 x 10²)(2 x 10^-5)

= 12 x 10^-3​

= 1.2 x 10^-2

​​​

400

(7.32 x 10⁹) divided by (9 x 10^-4)

= 0.813 x 10¹³

= 8.13 x 10¹²

500

(6.7 x 10^-4) - (2.3 x 10^-3)

= (0.67 x 10^-3) - (2.3 x 10^-3)

= -1.63 x 10^-3

Adding & Subtracting Polynomials

100

Simplify, and write in standard form:

(5x + 3) + (7 - 9x)

= 5x + 3 + 7 - 9x

= -4x + 10

200

(5x² - 3x + 4) - (4x² + 7x - 2)

= 5x² - 3x + 4 - 4x² - 7x + 2

= x² -10x + 6

300

(6p + 7) - (12 + 6p)

= 6p + 7 - 12 - 6p

= -5

400

(3a² - 4 - 3a) - (5a + 5a² - 7)

= 3a² - 4 - 3a - 5a - 5a² + 7

= -2a² - 8a + 3

500

(11 - 8p - 8p²) + (p - 3p² - 25)

= 11 - 8p - 8p² + p - 3p² - 25

= -11p² - 7p - 14