Expanding, Factorising and Index Laws 1 and 2

Expanding

100

Expand the following:

-2(x + 4)

-2x - 8

200

Expand the following:

(2x-1)(x+5)

2x² + 9x - 5

300

Expand the following:

(3a + 2b)²

9a² + 6ab + 4b²

400

Expand the following:

(x-5)(x+5)

x² - 25

500

Expand and simplify:

(2x - 1)² - 4x²

-4x + 1

Factorising

100

Factorise:

3x + 12

3(x + 4)

200

Factorise:

2(a - 3) - x(a - 3) - c(a - 3)

(a - 3)(2 - x - c)

300

Factorise:

16x² - 49

(4x - 7)(4x+ 7)

400

Factorise:

x² + 4x + 3

(x + 1)(x + 3)

500

Can this trinomial be factorised:

x² + 7x - 6

NO

Nothing multiplies to give (-6), but adds to (+7)

Index Law 1

100

Simplify:

5⁶ x 5⁵

5¹¹

200

Simplify:

t³ x t⁷

t¹⁰

300

Simplify:

b x b⁵ x b²

b⁸

400

Simplify:

3m³ x 5m⁹

15m¹²

500

Simplify:

4e⁴ f² x 2e² f²

8e⁶ f⁴

Index Law 2

100

Simplify:

10⁶ / 10⁵

10

200

Simplify:

d⁸ / d³

d⁵ 

300

Simplify:

8b¹⁰ / 4b⁵

2b⁵

400

Simplify:

4a⁴ / 20a³

a / 5

500

Simplify:

8m⁵ n⁴ / 6m⁴ n³

4mn / 3

Index Laws

100

b⁵ x b² / b

b⁶

200

t⁴ x t³ / t⁶

t

300

(a⁴ / b³) x (b⁶ / a)

a³ b³

400

(4d²e x 9d³e²) / 3de

12d⁴e²

500

(12m⁷n³ / 5m⁴n) x (25m²n³ / 8mn⁴)

15m⁴n / 2