Expanding Brackets Objectives D Grade Multiply out expressions

Expanding Brackets Objectives: D Grade Multiply out expressions with brackets such as: 3(x + 2) or 5(x - 2) Factorise expressions such as 6 a + 8 and x 2 – 3 x C Grade Expand (and simplify) harder expressions with brackets such as: x(x 2 - 5) and 3(x + 2) - 5(2 x – 1) Prior knowledge: Understand that 2 x means x + x x 2 means x × x cab = abc because multiplication is commutable Be able to collect terms Use the grid method for multiplying

Expanding Brackets What are brackets and why use them? Example 1 3(xx + 33) A number or letter / term next to brackets means 3 of whatever is in the brackets Collecting terms we have: In other words: 3 x + 9 3 × (xx + 33) × This can be put into the grid method 3 x Using the grid method we add the answers in the grid Because 3 x and 9 have different powers of x (there is no x in the term 9) we leave the answer as it is 9 +

Expanding Brackets Example 2 x × (xx + 33) Remember x × x = × x 2 Example 3 3 x + x × (xx 2+ 33) Remember x × x 2= x 3 × x 3 3 x +

Now do these: Expanding Brackets 1. 2(x + 3) 2. 2(t + 1) 3. 3(d − 4) 4. − 2(x + 1) -2 x - 2 2 t + 2 3 d - 12 2 x + 6 5. 4(y + 4) 6. 6(h − 2) 7. 5(3 ab + 2 a) 8. − 3(p − 2) -3 p - 6 6 h - 12 15 ab+ 5 a 4 y + 16 9. p(p + 2) 10. b(2 b + 3) 11. w(2 w − 3) 12. t(3 t − 4) 2 b 2 + 3 b 2 w 2 – 3 w p 2 + 2 p 3 t 2 – 4 t 13. p(p 2 + 4) 14. w(w 2 − 3) 15. x(xy − xy 2) w 3 – 3 w p 3 + 4 p x 2 y + x 2 y 2 16. ct 2 (t − 3) 17. fp(p 3 − p) 18. xyz(xz + yz) fp 4 – fp 2 ct 3 – 3 ct 2 x 2 yz 2 + xy 2 z 2