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Simplify the following expressions by multiplying out the brackets: 3.2 20(a+2b), 3.3 15(2b+3c), 3.4 -5(k+m), 3.5 -6(3a+2c), 3.6 (4p-9q)10, 3.7 (7x-12y)-3, 3.8 -2(2k+3m-n), 3.9 2a(5a2-3a-1)

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: Multiplying Out Brackets

3.2 20(a+2b)20(a+2b)

  1. Distribute the 20 to each term inside the bracket.

    20(a+2b)=20×a+20×2b20(a+2b) = 20 \times a + 20 \times 2b 20(a+2b)=20a+40b20(a+2b) = 20a + 40b

    The answer is 20a+40b\boxed{20a+40b}.

    3.3 15(2b+3c)15(2b+3c)

  2. Distribute the 15 to each term inside the bracket.

    15(2b+3c)=15×2b+15×3c15(2b+3c) = 15 \times 2b + 15 \times 3c 15(2b+3c)=30b+45c15(2b+3c) = 30b + 45c

    The answer is 30b+45c\boxed{30b+45c}.

    3.4 −5(k+m)-5(k+m)

  3. Distribute the −5-5 to each term inside the bracket.

    −5(k+m)=−5×k+(−5)×m-5(k+m) = -5 \times k + (-5) \times m −5(k+m)=−5k−5m-5(k+m) = -5k - 5m

    The answer is −5k−5m\boxed{-5k-5m}.

    3.5 −6(3a+2c)-6(3a+2c)

  4. Distribute the −6-6 to each term inside the bracket.

    −6(3a+2c)=−6×3a+(−6)×2c-6(3a+2c) = -6 \times 3a + (-6) \times 2c −6(3a+2c)=−18a−12c-6(3a+2c) = -18a - 12c

    The answer is −18a−12c\boxed{-18a-12c}.

    3.6 (4p−9q)10(4p-9q)10

  5. Distribute the 10 to each term inside the bracket.

    (4p−9q)10=4p×10−9q×10(4p-9q)10 = 4p \times 10 - 9q \times 10 (4p−9q)10=40p−90q(4p-9q)10 = 40p - 90q

    The answer is 40p−90q\boxed{40p-90q}.

    3.7 (7x−12y)−3(7x-12y)-3

  6. Distribute the −3-3 to each term inside the bracket.

    (7x−12y)−3=7x×(−3)−12y×(−3)(7x-12y)-3 = 7x \times (-3) - 12y \times (-3) (7x−12y)−3=−21x+36y(7x-12y)-3 = -21x + 36y

    The answer is −21x+36y\boxed{-21x+36y}.

    3.8 −2(2k+3m−n)-2(2k+3m-n)

  7. Distribute the −2-2 to each term inside the bracket.

    −2(2k+3m−n)=−2×2k+(−2)×3m−(−2)×n-2(2k+3m-n) = -2 \times 2k + (-2) \times 3m - (-2) \times n −2(2k+3m−n)=−4k−6m+2n-2(2k+3m-n) = -4k - 6m + 2n

    The answer is −4k−6m+2n\boxed{-4k-6m+2n}.

    3.9 2a(5a2−3a−1)2a(5a^2-3a-1)

  8. Distribute the $2a$ to each term inside the bracket.

    2a(5a2−3a−1)=2a×5a2−2a×3a−2a×12a(5a^2-3a-1) = 2a \times 5a^2 - 2a \times 3a - 2a \times 1 2a(5a2−3a−1)=10a3−6a2−2a2a(5a^2-3a-1) = 10a^3 - 6a^2 - 2a

    The answer is 10a3−6a2−2a\boxed{10a^3-6a^2-2a}.

    : Revision of Addition and Subtraction of Integers

    4.1 3+23+2

  9. Add the numbers.

    3+2=53+2 = 5

    The answer is 5\boxed{5}.

    4.2 3−23-2

  10. Subtract the numbers.

    3−2=13-2 = 1

    The answer is 1\boxed{1}.

    4.3 2−32-3

  11. Subtract the numbers.

    2−3=−12-3 = -1

    The answer is −1\boxed{-1}.

    4.4 −3+2-3+2

  12. Add the numbers.

    −3+2=−1-3+2 = -1

    The answer is −1\boxed{-1}.

    4.5 −3−2-3-2

  13. Subtract the numbers.

    −3−2=−5-3-2 = -5

    The answer is −5\boxed{-5}.

    4.6 6−(−4)6-(-4)

  14. Change subtraction of a negative to addition of a positive.

    6−(−4)=6+46-(-4) = 6+4

  15. Add the numbers.

    6+4=106+4 = 10

    The answer is 10\boxed{10}.

    4.7 1−51-5

  16. Subtract the numbers.

    1−5=−41-5 = -4

    The answer is −4\boxed{-4}.

    4.8 −1−5-1-5

  17. Subtract the numbers.

    −1−5=−6-1-5 = -6

    The answer is −6\boxed{-6}.

    4.9 1−(−5)1-(-5)

  18. Change subtraction of a negative to addition of a positive.

    1−(−5)=1+51-(-5) = 1+5

  19. Add the numbers.

    1+5=61+5 = 6

    The answer is 6\boxed{6}.

    4.10 4−64-6

  20. Subtract the numbers.

    4−6=−24-6 = -2

    The answer is −2\boxed{-2}.

    4.11 −6+3-6+3

  21. Add the numbers.

    −6+3=−3-6+3 = -3

    The answer is −3\boxed{-3}.

    4.12 2−72-7

  22. Subtract the numbers.

    2−7=−52-7 = -5

    The answer is −5\boxed{-5}.

    4.13 1−21-2

  23. Subtract the numbers.

    1−2=−11-2 = -1

    The answer is −1\boxed{-1}.

    4.14 −4−2-4-2

  24. Subtract the numbers.

    −4−2=−6-4-2 = -6

    The answer is −6\boxed{-6}.

    4.15 8−108-10

  25. Subtract the numbers.

    8−10=−28-10 = -2

    The answer is −2\boxed{-2}.

    4.16 −9+4-9+4

  26. Add the numbers.

    −9+4=−5-9+4 = -5

    The answer is −5\boxed{-5}.

    4.17 −10+6+1-10+6+1

  27. Add the first two numbers.

    −10+6=−4-10+6 = -4

  28. Add the result to the last number.

    −4+1=−3-4+1 = -3

    The answer is −3\boxed{-3}.

    4.18 −7−3+4-7-3+4

  29. Subtract the first two numbers.

    −7−3=−10-7-3 = -10

  30. Add the result to the last number.

    −10+4=−6-10+4 = -6

    The answer is −6\boxed{-6}.

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