Many + lots method (x+3)(x+2) = x(x+2) + 3(x+2) = x2 + 2x + 3x + 6 = x2 + 5x + 6
Face method(x+3)(x+2) = x2 + 6 + 3x + 2x = x2 + 6 + 5x = x2 + 5x + 6
Exercises in multiplying pairs of brackets: whichever method you prefer, your eventual answer should be in the x2 + 5x + 6 form.
1 (x + 2)(x + 3) 11 (3x + 1)(x + 2) 21 (5x + 2)(5x - 2)
2 (x + 3)(x + 4) 12 (3x + 1)(3x + 1) 22 (3x + 2)(3x - 2)
3 (x + 4)(x + 5) 13 (x + 2)(4x + 3) 23( 7x + 12)(7x - 12)
4 (x + 2)(x + 1) 14 (x - 2)(x + 3) 24 (5x + 20)(5x - 20)
5 (x + 1)(x + 1) 15 (x - 2)(x - 3) 25 (5x + 2)(x - 2)
6 (x + 1)(x + 3) 16 (x - 2)(x - 3) 26 3(x + 4)(x - 2)
7 (x + 4)(x + 3) 17 (3x - 2)(x - 3) 27 12(x + 2)(x - 2)
8 (x + 12)(x + 3) 18 (x - 1)(x - 3) 28 (3x + 4)(5x - 2)
9 (x + 4)(x + 9) 19 (x + 2)(x - 3) 29 (5x + 21)(5x - 21)
10 (x + 10)(x + 10) 20 (3x + 2)(4x - 3) 30 (px + q)(px - q)
If you let x = 10 for 1 to 10 above, you can check your answers by doing this arithmetic in 31 to 40. For 41 to 60 use the algebra technique to make the arithmetic simpler, for example
103 x 102 = (100 +3)(100 +2) = 100² + 6 + 300 + 200 = 10000+500+6 = 10506
31 (10 + 2)(10+ 3) 41 (30 + 1)(10 + 2) 51 52 x 51
32 (10 + 3)(10 + 4) 42 (30 + 1)(30 + 1) 52 52 x 52
33 (10 + 4)(10 + 5) 43 (10 + 2)(10 + 3) 53 71 x 71
34 (10 + 2)(10 + 1) 44 (10 + 3)(10 + 3) 54 99 x 99
35 (10 + 1)(10 + 1) 45 (10 + 4)(10 + 4) 55 1012 x 1012
36 (10 + 1)(10 + 3) 46 (100 + 3)(100 + 3) 56 29 x 31
37 (10 + 4)(10 + 3) 47 (100 - 3)(100 + 3) 57 18 x 22
38 (10 + 12)(10 + 3) 48 (100 + 5)(100 + 5) 58 28 x 32
39 (10 + 4)(10 + 9) 49 (50 + 3)(50 + 3) 59 109 x 991
40 (10 + 10)(10 + 10) 50 (30 + 2)(40 - 3) 60 1012 x 988
By now you should be seeing ways of doing arithmetic in lots of ways, so this next set offer a variety of methods. Make sure you show enough working to communicate the method you have picked. Calculators are completely unnecessary; you should have an idea at least of the last digit and the right size of answer.
61 61² 71 907 x 907 81 9⁴ = 81 x 81
62 161² 72 907 x 913 82 (10-3)(50-1)
63 104 x 96 73 907 x 893 83 7.1 ²
64 105 x 95 74 93² 84 0.71²
65 35² 75 907 x 1093 85 0.071²
66 35 x 45 76 24² 86 0.99²
67 36 x 34 77 1024² 87 1.018 x 1.022
68 33 x 37 78 976² 88 0.28 x 0.32
69 320 x 380 79 79² 89 1.09 x 9.91
70 321 x 381 80 179 x 21 90 10.12 x 98.8
