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Simplify the following expressions and determine if terms are like or unlike: a) 2ab and 2ab2 b) 4xy and -9xy Simplify: (3a)2 + 7a(5a - 12b) 7k + 4m2 - 2k + 10m2 (2x - 1)(2x - 4)

Mathematics

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QUESTION 4

4.1 Are these like or unlike terms?

a) 2ab2ab and 2ab22ab^2
These are unlike terms because the powers of the variable bb are different (b1b^1 vs b2b^2).

b) 4xy4xy and −9xy-9xy
These are like terms because they have the exact same variables (xx and yy) raised to the same powers (x1y1x^1y^1).

4.2 Simplify the following expressions:

4.2.1 (3a)2+7a(5a−12b)(3a)^2 + 7a(5a - 12b)

  1. Simplify the squared term and distribute $7a$.

    (3a)2+7a(5a−12b)=(32a2)+(7a⋅5a)−(7a⋅12b)(3a)^2 + 7a(5a - 12b) = (3^2 a^2) + (7a \cdot 5a) - (7a \cdot 12b) =9a2+35a2−84ab= 9a^2 + 35a^2 - 84ab
  2. Combine like terms.

    =(9+35)a2−84ab= (9+35)a^2 - 84ab =44a2−84ab= 44a^2 - 84ab 44a2−84ab\boxed{44a^2 - 84ab}

    4.2.2 7k+4m2−2k+10m27k + 4m^2 - 2k + 10m^2

  3. Group like terms.

    =(7k−2k)+(4m2+10m2)= (7k - 2k) + (4m^2 + 10m^2)
  4. Combine like terms.

    =(7−2)k+(4+10)m2= (7-2)k + (4+10)m^2 =5k+14m2= 5k + 14m^2 5k+14m2\boxed{5k + 14m^2}

    4.2.3 (2x−1)(2x−4)(2x - 1)(2x - 4)

  5. Use the distributive property (FOIL method).

    =(2x)(2x)+(2x)(−4)+(−1)(2x)+(−1)(−4)= (2x)(2x) + (2x)(-4) + (-1)(2x) + (-1)(-4) =4x2−8x−2x+4= 4x^2 - 8x - 2x + 4
  6. Combine like terms.

    =4x2+(−8−2)x+4= 4x^2 + (-8-2)x + 4 =4x2−10x+4= 4x^2 - 10x + 4 4x2−10x+4\boxed{4x^2 - 10x + 4}
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