## Algebra practice

By popular request… Remember that a multiplying mixed signs gives a negative answer and multiplying same signs gives a positive answer!

### Multiply out the following

- 2(3x – 2) – 4(2x – 1)
- 2xy(x + y)
- 2(4x + 3) + 3(2x – 9)
- 4(x + y) – 2(x + 2y)
- 2x(x
^{2}– y^{3}) - 2(5x – 4) – 3(2x + 7)
- 4(10x + 3y) – 7(x + y)
- 3x
^{2}(4x + 2y) – 4y(2x^{2}– 3y) - 2(x – y) – (4x + 3y)
- 14(2x – y) – 5(3x – 2y) + 4(4y – 2x)

### Factorise the following expressions

- remember to find the largest common denominator and to divide through by the common denominator to find what goes inside the bracket
- remember that xy
^{2}means ‘x multiplied by y squared’ and is different to x^{2}y

- 6x
^{2}y – 9xy^{2} - 12xy – 15x
^{2}y^{2} - 18x
^{2}– 6x - 21p
^{2}+ 28p - 24q
^{2}– 18q - 15r
^{2}s – 10rs^{2} - 18xy – 27xy
^{2} - 15x
^{2}y^{3}– 20x^{3}y^{4} - 12py
^{2}– 9p^{2}y - 144x
^{4}y^{8}z^{3}– 84xy^{2}z