Learn – Algebra foundations – AS, M expressions

1 Lesson notes

  • An addition/subtraction (AS) expression is one where the last operation by PEMDAS rules is addition or subtraction.
  • A multiplication (M) expression is one where the last operation by PEMDAS rules is multiplication.
  • A division (D) expression is one where the last operation by PEMDAS rules is division.
  • An exponentiation (E) expression is one where the last operation by PEMDAS rules is exponentiation.

2 Exercises

2.1 Problem set

Classify each of the following as one of AS, M, D and E expressions.

  1. \frac{\sqrt{x+3}}{5x-\sqrt{x}} + \frac{3x}{9x^5+5}
  2. (x^2+3x+4)(x^4+4)
  3. \frac{2x^2+3}{5x-\sqrt{x}} - \frac{2^x}{x^5+5^x}
  4. xy+zw
  5. x^4+x^3
  6. (x+1)(y+1)

2.2 Problem set

Classify each of the following as one of AS, M, D and E expressions.

  1. x+\frac{x^4+1}{x^2+1}
  2. x^2(y+1)
  3. -x+(x+5)x^2
  4. x^3-x(y+1)+x^5
  5. \frac{x+1}{x+2}
  6. \frac{x^2+x}{x+2}

2.3 Problem set

Classify each of the following as one of AS, M, D and E expressions.

  1. \frac{x^4+1}{x^2+1}
  2. x^3y^3z^3
  3. \frac{a^5b^3}{c^7}
  4. (xyz)^2(xy)^3
  5. (x+y)^2

2.4 Problem set

Classify each of the following as one of AS, M, D and E expressions.

  1. (xyz)^3
  2. \left(\frac{xy}{abc}\right)^2
  3. \left(\frac{x+1}{x+2}\right)^2

2.5 Problem set

Classify each of the following as one of AS, M, D and E expressions.

  1. x(y+1)
  2. (p+3)q
  3. -c(a-b)
  4. (x^2+3x+4)(2x+3)-7
  5. 1+(2x-1)(3x-1)(5x-1)(6x-1)
  6. (x-7) + (1-3x)(4-x)(7x-3)
  7. (x-1)(2x-1)+(x-1)(9x^2-3)