Multi-variable Equations

FOIL

100

Use foil to multiply the two binomials.

(x + 1)(x + 1)

x² + 2x + 1

200

Use foil to multiply the two binomials.

(x - 3)(x + 8)

x² + 5x - 24

300

Use foil to multiply the two binomials.

(x - 4)(x - 5)

x² - 9x + 20

400

Use foil to multiply the two binomials.

(2x - 1)(3x + 4)

6x² + 5x - 4

500

Factor the polynomial below.  In other words, which two binomials did you multiply together to get this polynomial?

x² + 7x + 12

(x + 3)(x + 4)

Simplifying Exponents

100

Simplify.

x⁵x^-5

1

200

2x⁴y^-3

(2x^4)/y^3

300

-2xy^5*8x^-3y

(16y^6)/x^2

400

 (-14x^-3yz^3)/(2xy^-5) 

(-7y^4z^3)/x^4

500

((2x^5y^3)^3(4xy^4)^2)/(8x^7y^12)

16x¹⁰y⁵

Absolute Value

100

Solve for x.

|x| = 5

x = 5 or -5

200

Solve for x.

|x - 5| = 20

x = 25 or x = -15

300

Solve for x.

|-6x + 3| = 27

x = -4 or x = 5

400

|-2x + 7| + 5 = 14

x = -1 or x = 8

500

4|2x - 14| + 10 = 18

x = 7/2 or x = 8

Dividing Polynomials by Monomials

100

(18x^4y^9)/(3x^2y^6)

6x^2y^3

200

(6xy^2 - 12x^3y^4)/(3x)

2y² - 4x²y⁴

300

(2x^2y^5 + 6x^4y^4 + 2xy^3)/(2xy)

xy⁴ + 3x³y³ + y²

400

(-12a^5 + 30a^4 - 21a^3)/(3a^2)

-4a³ + 10a² - 7a

500

(-3a^11b^7 + 9a^8b^6 - a^4b^2 + a^2b^2)/(-a^2b^2)

3a^9b^5 - 9a^6b^4 + a^2 - 1

Solving for a Variable

100

Solve for r.

D = rt

r = D/t

200

Solve for m.

y = mx + b

m = (y-b)/x

300

Solve for h.

A = 1/2bh

h = (2A)/b

400

Solve for y.  

-6x + 2y = 12 - 2x

y = 2x + 6

500

Solve for w.

P = 2L + 2W

(P - 2L)/2