Learning Task 2: A.evaluate The Algebraic Expressions Learning Task 2:…

learning task 2: A.evaluate the algebraic expressions

learning task 2: B. perform the indicated operations

learning task 3: Solve the following
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ALGEBRAIC EXPRESSION

An algebraic expression is made up of numbers referred to as coefficients or constants and letters referred to as variables. An algebraic expression is parted into terms divided by the operator in the expression. An algebraic expression may also have exponents which make the expression more complex.

Answers with solutions:

A.

1. 3abc + bc – a

   (3*4*-5*0.6) + (-5*0.6) – (4)

   (-36) + (-3) – (4)

  -43

2. bxy + 5ab – ay

   (-5*-3*0.4) + (5*4*-5) – (4*0.4)

   (6) + (-100) – (1.6)

   -95.6    

3. abz – 8z + b

   (4*-5*0.5) – (8*0.5) + (-5)

   (-10) – (4) + (-5)

  -19

4. ax + by – cz

   (4*-3) + (-5*0.4) – (0.6*0.5)

   (-12) + (-2) – (0.3)

   -14.3

5. 4ax + cz

   (4*4*-3) + (0.6*0.5)

   (-48) + (0.3)

  -47.7

6. 3x² + 2xy – 3(ab)²

   (3*(-3*-3)) + (2*-3*0.4) – (3*((4*-5)*(4*-5)))

   (3*9) + (2*-3*0.4) – (3*(-20*-20))

   (3*9) + (2*-3*0.4) – (3*400)

   (27) + (-2.4) – (1200)

   -1,175.4

7. 25 – 2x²y + 3a²b – az²

   (25) – (2*(-3*-3)*0.4) + (3*(4*4)*-5) – (4*(0.5*0.5))

   (25) – (2*9*0.4) + (3*16*-5) – (4*0.25)

   (25) – (7.2) + (-240) – (1)

   -223.2

8. (az)² + 5x²y – 4bc

   ((4*0.5)*(4*0.5)) + (5*(-3*-3)*0.4) – (4*-5*0.6)

   (2*2) + (5*9*0.4) – (4*-5*0.6)

   (4) + (18) – (-12)

   34

9. 2x²y² – 12abz – 16

   (2*(-3*-3)*(0.4*0.4)) – (12*4*-5*0.5) – (16)

   (2*9*0.16) – (12*4*-5*0.5) – (16)

   (2.88) – (-120) – (16)

  106.88

10. 8z³ – 4x + y²

   (8*(0.5*0.5*0.5)) – (4*-3) + (0.4*0.4)

   (8*0.125) – (4*-3) + (0.4*0.4)

   (1) – (-12) + (0.16)

   13.16

B.

1. (5x⁴ – 3x² + 4) + (6x³ – 4x² – 7)

   5x⁴ + 6x³ – 3x² – 4x² + 4 – 7

   5x⁴ + 6x³ – 7x² – 3

2. (-7x³y + 4x²y² – 2) + (4x³y + 1 – 8x²y²)

   -7x³y + 4x³y + 4x²y² – 8x²y² – 2 + 1

  -3x³y – 4x²y² – 1

3. (5 + 24y³ – 7y²) + (-6y³ + 7y² + 5)

   24y³ – 6y³ – 7y² + 7y² + 5 + 5

   18y³ + 10

4. (2x⁵ – 6x³ – 12x² – 4) + (-11x⁵ + 8x + 2x²  + 6)

   2x⁵- 11x⁵ – 6x³ – 12x² + 2x² + 8x – 4 + 6

   -9x⁵ – 6x³ – 10x² + 8x + 2

5. (3y⁵ – 2y + y⁴  + 2y³ + 5) + (2y⁵ + 3y³ + 2 + 7)

   3y⁵ + 2y⁵ + y⁴  + 2y³ + 3y³- 2y + 5 + 2 + 7

  5y⁵ + y⁴  + 5y³- 2y + 14

6. (5x³ – 7x² + 3x – 4) – (8x³ + 2x² + 3x – 7)

   5x³ – 8x³ – 7x² – 2x² + 3x – 3x – 4 + 7

  -3x³ – 9x² + 3

7. (2x²y – 5xy + 3y²) – (7xy – 6y² + 5x²y)

   2x²y – 5x²y – 5xy – 7xy + 3y² + 6y²  

   -3x²y – 12xy + 9y²

8. (9x⁵ – 6x³ + 7x²) – (7x³ – 6x⁵ + 2x²)

   9x⁵ + 6x⁵ – 6x³ – 7x³ + 7x² – 2x²

  15x⁵ – 13x³ + 5x²

9. (6x² – 3x + 8) – (4x³ – 5x – 8)

   6x² – 3x + 8 – 4x³ + 5x + 8

  – 4x³ + 6x² + 2x + 16

10. (1.5y³ + 4.8y² + 12) – (y³ – 1.7y² + 2y)

   1.5y³ – y³ + 4.8y² + 1.7y² – 2y + 12  

   0.5y³ + 6.5y² – 2y + 12

C.

1. Volume of a box = length * width * height = LWH

V = (2x – 3) * (x + 5) * (3x + 1)

V = (2(3) – 3) * ((3) + 5) * (3(3) + 1)

V = (6 – 3) * (3 + 5) * (9 + 1)

V = 3*8*10

V = 240cm³

2. Area of a triangle = (base * height) / 2

A = (10 *6) ÷ 2

A = 60 ÷ 2

A = 30cm²

3. Perimeter of a rectangle = 2L + 2W

P = (2*(x² + 2x – 3)) + (2*(5x + 4))

P = (2x² + 4x – 6) + (10x + 8)

P = 2x² + 4x – 6 + 10x + 8

P = 2x² + 14x + 2

4. ((3x³ + 7x² – 5) + (2x² + 3x + 8)) – (5x² + x – 5)

(3x³ + 7×2 – 5 + 2×2 + 3x + 8) – (5×2 + x – 5)

(3x³ + 7x² + 2x² + 3x – 5 + 8) – (5x² + x – 5)

(3x³ + 9x² + 3x + 3) – (5x² + x – 5)

3x³ + 9x² + 3x + 3 – 5x² – x + 5

3x³ + 9x²– 5x² + 3x – x + 3 + 5

3x³ + 4x² + 2x + 8

5. (4x³ + x² + 5) – (3x³ + 4x² – 7)

4x³ + x² + 5 – 3x³ – 4x² + 7

4x³ – 3x³ + x² – 4x² + 5 + 7

x³ – 3x² + 12

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