Yr 9 Algebra

Expanding (FOIL, DOTS, Perfect squares)

100

(x+1)(x+4)

x²+4x+x+4
=x²+5x+4

150

(x+7)²

x²+14x+49

200

(x+9)(x-9)

x²-9²
=x²-81

250

(4x-2)²

=(4x)² -16x+2²
=4x²-16x+4

300

(5a-4b)(5a+4b)

25a²-16b²

350

(3x-y)(8x-6y)

= 24x²-18xy-8xy+6y²

= 24x²-26xy+6y²

Simplifying Algebra

100

Simplify:     6x + 5x

11x

150

Simplify:      6x - 2y - 4x

2x - 2y

200

Simplify:    2A + 5B + 6A + 2A - 3B

10A + 2B

250

Simplify:     5 x 5r + 2r

27r

300

Simplify:    2x² + 4x - 3x²

4x - x²

350

Simplify 7pu−3+9up+6

16pu + 3

Expanding with Distributive Law

100

5(x + 4)

5x + 20

150

6y (3y + 4)

18y² + 24y 

200

4(2x + 2)

8x + 8

250

-3(x - 5)

-3x + 15

300

8x^2 (2x - 5y)

16x^3 - 40x^2y

350

5(t - 4) + 7t (5 + 10)

5t - 20 + 35t + 70t

110t - 20

Factorising Common Factors

100

10x + 20

10 (x + 2)

150

ab - ac

a(b - c)

200

28x + 14

7(4x + 2)

250

27xy + 18x + 9xyz

9x (3y + 2 + yz)

300

12nm - 24n²m²

12nm(1 - 2nm)

350

36x^2 + 54x - 72x

9x (4x + 6 - 8)

9x (4x -2)

factorising DOTS

100

x²-4

(x+2)(x-2)

150

25x²-16

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

200

(x+5)²-9

(x+5+3)(x+5-3)
=(x+8)(x+2)

250

3x²-12
*hint - take common factor 1st

3(x²-4)
=3(x+2)(x-2)

300

5x²-5
*hint: common factor

5(x²-1)
=5(x+1)(x-1)

350

49-(x+3)²

(7+(x+3))(7-(x+3))
=(7+x+3)(7-x-3)
=(x+10)(-x+4)