ALGE-BRUH

Expanding Algebra

100

Expand a(a+7)

a² + 7a 

200

Expand and simplify a(a+5)+7(a+6)

a² + 12a + 42

300

Expand and simplify  4m(2m - 6) - 6(4m - 5)

8m² - 48m +30

400

Expand and simplify (5n - 4)(7n - 2)

35n² - 38n + 8

500

Expand and simplify (x + 2)²

x² + 4x + 4

Indices

100

Simplify m⁵ * m² * m

m⁸

200

Simplify 12m⁴ / 3m²

4m²

300

Evaluate 7a⁰-(2b⁰)²

3

400

Simplify (-3x²y)³

-27x⁶y³

500

Simplify using positive indices r³s^-2

r³/s² 

Surds

100

Simplify sqrt(40) 

2 sqrt(10)

200

Simplify sqrt(8) - 6*sqrt(8) +15*sqrt(8)

10sqrt(8)

300

Simplify 5*sqrt(3) * 3*sqrt(5) 

15sqrt(15)

400

Simplify 5sqrt(18) / 24sqrt(175) 

sqrt(2)/8*sqrt(7) 

500

Expand and simplify (sqrt(6) - sqrt(15))(sqrt(3) -sqrt(2)) 

3sqrt(2) - 2sqrt(3) - 3sqrt(5) + sqrt(30)

Factorising Algebra

100

Factorise fully 12x²y - 8xy

4xy(3x - 2) 

200

Factorise by taking out a negative HCF  -3a² - 9ab

-3a(a + 3b) 

300

Factorise p⁴ - 16 

(p² + 4)(p² - 4)

400

Factorise fully 14ac + 7bc - 6ad - 3bd

(2a+b)(7c-3d)

500

Factorise x² - 2x - 8

(x - 4)(x + 2)

Algebraic Fractions

100

Simplify 4/x * 3/y

12/xy

200

Simplify 3x/5 divided by 2y/x 

3x²/10y 

300

Simplify 2y/5 + y/15

7y/15

400

Simplify 7a/12 - 5a/18

11a/36

500

Simplify 1/x  + 1/(x+1)

(2x+1)/(x*(x+1))