Learn – Algebra foundations – AS, M expressions

1 Lesson notes
2 Exercises

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.

Exercises

Problem set

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

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

Problem set

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

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

Problem set

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

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

Problem set

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

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

Problem set

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

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