Monomials
The number of "likes" a post gains in a week could be modelled with a monomial such as $-\frac{3}{5}x^2y^3z$. You already know how to read monomials from 2nd and 3rd ESO; here we review quickly and add letters and slightly more complicated coefficients.
Coefficient, literal part and degree
Identify the coefficient, the variable part and the degree of the monomial $-\frac{3}{5}x^2y^3z$.
Identify the coefficient, the variable part and the degree of the monomial $-\frac{3}{5}x^2y^3z$.
Like monomials
$5x^2y$ and $-2yx^2$ are like monomials (the order of the letters does not matter). $5x^2y$ and $5xy^2$ are not: the exponents do not match letter by letter.
Check whether the monomials $A = 5x^2y$ and $B = -2yx^2$ are like terms. If so, calculate their sum $A + B$ and their difference $A - B$.
Check whether the monomials $A = 5x^2y$ and $B = -2yx^2$ are like terms. If so, calculate their sum $A + B$ and their difference $A - B$.
Numerical value
To calculate the numerical value of a monomial with several letters, substitute each letter with its value (in brackets if it is negative) and calculate.
Find the numerical value of the monomial $M(x,y) = 4x^2y^3$ for the values $x = -2$ and $y = 3$.
Find the numerical value of the monomial $M(x,y) = 4x^2y^3$ for the values $x = -2$ and $y = 3$.
Translating sentences into a monomial
Many problems describe a monomial in words. You translate "from the inside out": first what is closest to each number, then the rest.
Write the monomial that mathematically represents the following statement: "Half the product of the square of a number and the cube of a different number".
Write the monomial that mathematically represents the following statement: "Half the product of the square of a number and the cube of a different number".