Monomials
The profit for each download of a game in an app store is expressed by the monomial $7x^2y$. Before doing any calculation with it, you need to know how to read it: which part is the number and which part is the letters.
What a monomial is
In an app store, the profit per game download is expressed by the monomial $7x^2y$. Identify the following elements of this expression: Coefficient: Literal part: Degree…
In an app store, the profit per game download is expressed by the monomial $7x^2y$. Identify the following elements of this expression:
-
Coefficient:
-
Literal part:
-
Degree of the monomial:
Like monomials
$5x^2$ and $-2x^2$ are like monomials. $5x^2$ and $5x$ are not, even though they look similar: the exponents do not match.
We are organising an inventory of robotics parts. Group the following monomials into pairs of like terms: $5x^2$, $-3ab$, $x$, $\frac{1}{2}ab$, $-2x^2$, $8x$
We are organising an inventory of robotics parts. Group the following monomials into pairs of like terms:
$5x^2$, $-3ab$, $x$, $\frac{1}{2}ab$, $-2x^2$, $8x$
The numerical value of a monomial
To work out the numerical value of a monomial, substitute each letter with its value (in brackets if it is negative) and calculate.
Calculate the numerical value of the monomial $M(x) = -5x^2$ for the indicated values of the variable: a) $x = 2$ b) $x = -1$ c) $x = 0$
Calculate the numerical value of the monomial $M(x) = -5x^2$ for the indicated values of the variable:
- a) $x = 2$
- b) $x = -1$
- c) $x = 0$
Adding and subtracting like monomials
$$4x + 2x - x = (4 + 2 - 1)x = 5x$$Simplify the following algebraic expressions by adding and subtracting like monomials: a) $4x + 2x - x$ b) $5a^2 - 3a^2 + 7a^2$ c) $3ab + ab - 2ab$
Simplify the following algebraic expressions by adding and subtracting like monomials:
- a) $4x + 2x - x$
- b) $5a^2 - 3a^2 + 7a^2$
- c) $3ab + ab - 2ab$
Monomials in areas, perimeters and sentences
The dimensions of a shape can be monomials. The area of a rectangle with base $5x$ and height $3x$ is $5x \cdot 3x = 15x^2$: you will see this in detail in the section on operations with monomials, but you can already identify which monomial corresponds to each quantity.
Look at the following regular hexagon whose side measures $x$ metres. Write the monomial representing its perimeter and calculate its value if each side were $4,5$ cm.
Look at the following regular hexagon whose side measures $x$ metres. Write the monomial representing its perimeter and calculate its value if each side were $4,5$ cm.
Translate the following phrases into algebraic language using a single monomial: a) Double the cube of a number $x$. b) Half the product of two numbers $a$ and $b$. c)…
Translate the following phrases into algebraic language using a single monomial:
- a) Double the cube of a number $x$.
- b) Half the product of two numbers $a$ and $b$.
- c) Three times the square of the distance $d$.
Back to the start: In the monomial $7x^2y$, the coefficient is the number $7$, the literal part is the letters $x^2y$ and its degree is $2 + 1 = 3$.