Expanding Brackets Objectives: D GradeMultiply out expressions with brackets such as: 3(x + 2) or 5(x - 2) Factorise expressions such as 6a + 8 and x 2 – 3x C GradeExpand (and simplify) harder expressions with brackets such as: x(x 2 - 5) and 3(x + 2) - 5(2x – 1) Prior knowledge: Understand that 2x 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(x + 3) A number or letter / term next to brackets means 3 of whatever is in the brackets x + 3 In other words:3 × (x + 3) This can be put into the grid method × 3 x3 Collecting terms we have:3x + 9 3x3x9 Using the grid method we add the answers in the grid 3x3x9 + Because 3x and 9 have different powers of x (there is no x in the term 9) we leave the answer as it is

Expanding Brackets Example 2 x × (x + 3) × x x 3 x2x2 3x3x x2x2 3x3x + Remember x × x = x 2 Example 3 x × (x 2 + 3) × x x2x2 3 x3x3 3x3x x3x3 3x3x + Remember x × x 2 = x 3

Expanding Brackets Now do these: 1.2(x + 3) 2. 2(t + 1) 3. 3(d − 4) 4. − 2(x + 1) 5. 4(y + 4) 6. 6(h − 2) 7. 5(3ab + 2a) 8. − 3(p − 2) 9.p(p + 2)10. b(2b + 3) 11. w(2w − 3) 12. t(3t − 4) 13. p(p 2 + 4) 14. w(w 2 − 3) 15. x(xy − xy 2 ) 16. ct 2 (t − 3) 17. fp(p 3 − p) 18. xyz(xz + yz) p 3 + 4p 2x + 6 x 2 yz 2 + xy 2 z 2 15ab+ 5a 2t + 2 3d x - 2 4y h p - 6 w 3 – 3w x 2 y + x 2 y 2 ct 3 – 3ct 2 fp 4 – fp 2 p 2 + 2p 2b 2 + 3b 2w 2 – 3w 3t 2 – 4t