This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Exercise 3: Multiplying Out Brackets 3.2 20(a+2b) Step 1: Distribute the 20 to each term inside the bracket. 20(a+2b) = 20 × a + 20 × 2b 20(a+2b) = 20a + 40b The answer is 20a+40b. 3.3 15(2b+3c) Step 1: Distribute the 15 to each term inside the bracket. 15(2b+3c) = 15 × 2b + 15 × 3c 15(2b+3c) = 30b + 45c The answer is 30b+45c. 3.4 -5(k+m) Step 1: Distribute the -5 to each term inside the bracket. -5(k+m) = -5 × k + (-5) × m -5(k+m) = -5k - 5m The answer is -5k-5m. 3.5 -6(3a+2c) Step 1: Distribute the -6 to each term inside the bracket. -6(3a+2c) = -6 × 3a + (-6) × 2c -6(3a+2c) = -18a - 12c The answer is -18a-12c. 3.6 (4p-9q)10 Step 1: Distribute the 10 to each term inside the bracket. (4p-9q)10 = 4p × 10 - 9q × 10 (4p-9q)10 = 40p - 90q The answer is 40p-90q. 3.7 (7x-12y)-3 Step 1: Distribute the -3 to each term inside the bracket. (7x-12y)-3 = 7x × (-3) - 12y × (-3) (7x-12y)-3 = -21x + 36y The answer is -21x+36y. 3.8 -2(2k+3m-n) Step 1: Distribute the -2 to each term inside the bracket. -2(2k+3m-n) = -2 × 2k + (-2) × 3m - (-2) × n -2(2k+3m-n) = -4k - 6m + 2n The answer is -4k-6m+2n. 3.9 2a(5a^2-3a-1) Step 1: Distribute the 2a to each term inside the bracket. 2a(5a^2-3a-1) = 2a × 5a^2 - 2a × 3a - 2a × 1 2a(5a^2-3a-1) = 10a^3 - 6a^2 - 2a The answer is 10a^3-6a^2-2a. Exercise 4: Revision of Addition and Subtraction of Integers 4.1 3+2 Step 1: Add the numbers. 3+2 = 5 The answer is 5. 4.2 3-2 Step 1: Subtract the numbers. 3-2 = 1 The answer is 1. 4.3 2-3 Step 1: Subtract the numbers. 2-3 = -1 The answer is -1. 4.4 -3+2 Step 1: Add the numbers. -3+2 = -1 The answer is -1. 4.5 -3-2 Step 1: Subtract the numbers. -3-2 = -5 The answer is -5. 4.6 6-(-4) Step 1: Change subtraction of a negative to addition of a positive. 6-(-4) = 6+4 Step 2: Add the numbers. 6+4 = 10 The answer is 10. 4.7 1-5 Step 1: Subtract the numbers. 1-5 = -4 The answer is -4. 4.8 -1-5 Step 1: Subtract the numbers. -1-5 = -6 The answer is -6. 4.9 1-(-5) Step 1: Change subtraction of a negative to addition of a positive. 1-(-5) = 1+5 Step 2: Add the numbers. 1+5 = 6 The answer is 6. 4.10 4-6 Step 1: Subtract the numbers. 4-6 = -2 The answer is -2. 4.11 -6+3 Step 1: Add the numbers. -6+3 = -3 The answer is -3. 4.12 2-7 Step 1: Subtract the numbers. 2-7 = -5 The answer is -5. 4.13 1-2 Step 1: Subtract the numbers. 1-2 = -1 The answer is -1. 4.14 -4-2 Step 1: Subtract the numbers. -4-2 = -6 The answer is -6. 4.15 8-10 Step 1: Subtract the numbers. 8-10 = -2 The answer is -2. 4.16 -9+4 Step 1: Add the numbers. -9+4 = -5 The answer is -5. 4.17 -10+6+1 Step 1: Add the first two numbers. -10+6 = -4 Step 2: Add the result to the last number. -4+1 = -3 The answer is -3. 4.18 -7-3+4 Step 1: Subtract the first two numbers. -7-3 = -10 Step 2: Add the result to the last number. -10+4 = -6 The answer is -6. 3 done, 2 left today. You're making progress.