Algebra: Part II

FOILed Again

100

(x-8)(x-9)

x² - 9x - 8x + 72

x² - 17x + 72

200

(2x + 3)(x - 4)

2x² - 8x + 3x - 12

2x² - 5x - 12

300

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

6x² - 4x + 3x - 2

6x² - x - 2

400

(x² - 2)(x² - 4)

x⁴ - 4x² - 2x² + 8

x⁴ - 6x² + 8

500

(3x + 4y)(4x - 3y)

12x² - 9xy + 16xy - 12y

12x² + 7xy - 12y

Distributing 1 Factor

100

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

6x + 9y - 12z + 3

200

6x(3x² + 5x - 2)

18x³ + 30x² - 12

300

x(8x³ - 3x² + 2x - 5)

8x⁴ - 3x³ + 2x² - 5x

400

x²y(2xy² + 3xyz + y²z³)

2x³y³ + 3x³y²z + x²y³z³

500

-4y(3y⁴ - 2y² + 5y - 5)

-12y⁵ + 8y³ - 20y² + 20y

Squared, Cubed, etc.

100

(x + 5)²

(x² + 10x + 25)

200

(y + 4)³

y³ + 12y² + 48y + 64

300

(2y - 1)²

4y² - 2y - 2y + 1

4y² - 4y + 1

400

(3z + 1)³

27z³ + 27z² + 9z + 1

500

(z - 1)⁵

z⁵ - 5z⁴ + 10z³ - 10z² + 5z - 1

GCF

100

Find the GCF: 30x⁴y² - 20x⁵y³ + 50x^6y

10x⁴y(3y - 2xy +5x²)

200

24x²y³ - 42x³y²

6x²y²(4y - 7x)

300

14x³y / 21xy⁴

2x² / 3y³

400

15x²y³ / 20xy⁹

3x / 4y⁶

500

14a²b - 21a / 28ab²

2zb - 3 / 4b²

Factoring

100

4x² - 81

(2x + 9)(2x - 9)

200

64a² - y²

(8a + y)(8a - y)

300

49x²y² - 9z²w⁴

(7xy + 3zw²)(7xy - 3zw²)

400

x³ - 27

(x - 3)(x² + 3x + 9)

500

8 - y³

(2-y)(4 + 2y + y²)