Chapter 5 - Algebra (Expansion and Fractorization)

Distributive Law

100

Expand and Simplify

-4x(3x+2)

-12x²-8x

200

Expand and Simplify

4x(x-3)-2x(5-x)

6x²-22x

300

Expand and Simplify

7x-5x(x+1)

2x-5x²

400

Expand and Simplify: 

3x(x-3)-4x(5-x)

7x²-29x

500

Expand and Simplify

7x²-5x(x+2)    

2x²-10x

Equations Containing Brackets

100

Solve for x:

2(x+4)=3-x

`x=-5/3`

200

Solve for x:

3(1-x)=x+2

`x=1/4`

300

Solve for x:

-3(6x-2)-4x=-5

`x=1/2`

400

Solve for x:

4x-4(4-x)=x+12

x=4

500

Solve for the unknown:

When a number is decreased by 2 and then multiplied by 3, the result is 12 more than the original number. Find the number.

`3(x-2)=12+x`

`x=9`

Equations Containing Fractions

100

Solve for x:

`(2x+3)/4=(x-2)/3`

`x=-17/2`

200

Solve for x:

`(x-6)/5-(2x-1)/10=(x-1)/2`

`x=-6/5`

300

Solve for x:

`(3x-7)/2=(2x+2)/3`

x=5

400

Solve for x:

`(5x+4)/3=x/2`

`x=-8/7`

500

Solve for x:

`(x+5)/2-(x-2)/3=(4x)/4`

`x=38/10`

Difference of two Squares

100

Determine whether each of the following is a difference between two squares.

(4x+1)(4x-1)  

(4x)²-1²  YES

200

Determine whether each of the following is a difference between two squares.

(2x-3)(3x+2)

6x²-5x-6 NO

300

Determine whether each of the following is a difference between two squares.

(2a+3b)(2a-3b)

(2a)²-(3b)² YES

400

Determine whether each of the following is a difference between two squares.

(3a-3b)²

9a²-18ab+9b² NO

500

Determine whether each of the following is a difference between two squares.

(3x-2)(5x+3)

24x²-10x-6 NO

Factoring

100

Fully factorize the following:

5ab+10b²

5b(a+2b)

200

Fully factorize the following:

-15x-6x²y

-3x(5+2xy)

300

Fully factorize the following:

9x²+3x+18

3(3x²+x+6)

400

Fully factorize the following:

9(x+2)²-3(x+2)  

3(x+3)(3x+5)

500

Fully factorize the following:

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

(x+5)(-3x-12)