Operations with monomials
The price of an electronic component and the quantity sold of it can be written as monomials; to find the total revenue you have to multiply them. Here you revise the four basic operations with monomials, a little more general than in 2nd and 3rd ESO.
Adding and subtracting like monomials
$$3x^2y - 5x^2y + \frac{1}{2}x^2y = \left(3 - 5 + \frac{1}{2}\right)x^2y = -\frac{3}{2}x^2y$$Calculate the result of the following addition and subtraction of like monomials: $3x^2y - 5x^2y + \frac{1}{2}x^2y$
Calculate the result of the following addition and subtraction of like monomials:
$3x^2y - 5x^2y + \frac{1}{2}x^2y$
Identify which of the following monomials are like terms and simplify the expression: $4m^3n - 2mn^3 + 5m^3n + mn^3$
Identify which of the following monomials are like terms and simplify the expression:
$4m^3n - 2mn^3 + 5m^3n + mn^3$
Find the missing monomial in the following operation so that the equality is true: $7x^3 + (\dots) = -2x^3$
Find the missing monomial in the following operation so that the equality is true:
$7x^3 + (\dots) = -2x^3$
Multiplying monomials
$$(2ab^2) \cdot (-3a^2b) \cdot (4a) = (2 \cdot (-3) \cdot 4)\, a^{1+2+1}b^{2+1} = -24a^4b^3$$Multiply the following monomials and simplify the result: $(2ab^2) \cdot (-3a^2b) \cdot (4a)$
Multiply the following monomials and simplify the result:
$(2ab^2) \cdot (-3a^2b) \cdot (4a)$
A technology company sells electronic components. The selling price of each component is given by the monomial $P = 15x^2y$ euros. If in one month they sell a quantity…
A technology company sells electronic components. The selling price of each component is given by the monomial $P = 15x^2y$ euros. If in one month they sell a quantity of components equivalent to $Q = 4xy^3$, express the company's total revenue as a monomial.
Dividing monomials
$$\frac{-15x^4y^3z}{5x^2y} = \frac{-15}{5}\,x^{4-2}y^{3-1}z^{1-0} = -3x^2y^2z$$Perform the division of the following monomials: $\frac{-15x^4y^3z}{5x^2y}$
Perform the division of the following monomials:
$\frac{-15x^4y^3z}{5x^2y}$
Determine which monomial $4x^2$ must be multiplied by to obtain $-20x^5$ as a result.
Determine which monomial $4x^2$ must be multiplied by to obtain $-20x^5$ as a result.
Power of a monomial
$$(-2x^3y^2)^4 = (-2)^4 x^{3 \cdot 4} y^{2 \cdot 4} = 16x^{12}y^8$$Calculate the power of the following monomial: $(-2x^3y^2)^4$
Calculate the power of the following monomial:
$(-2x^3y^2)^4$
Combined operations
When several operations are mixed, the usual order of operations is followed: first powers, then products and quotients, and finally additions and subtractions if there are any.
Perform the following combined operations with monomials, respecting the order of operations: $2x \cdot (3x^2)^2 - 5x^2 \cdot (x^3)$
Perform the following combined operations with monomials, respecting the order of operations:
$2x \cdot (3x^2)^2 - 5x^2 \cdot (x^3)$
Perform the following combined operation with monomials involving fractional coefficients and simplify the result:…
Perform the following combined operation with monomials involving fractional coefficients and simplify the result:
$\left( \frac{2}{3} a^2b \right)^3 : \left( \frac{4}{9} a^4b^2 \right)$
Subtract the monomial $5a^3b^4$ from the product of the monomials $-2ab^2$ and $3a^2b^2$. Express the final simplified result.
Subtract the monomial $5a^3b^4$ from the product of the monomials $-2ab^2$ and $3a^2b^2$. Express the final simplified result.
Back to the start: If a component costs $2x$ euros and $100x^2$ units are sold, the total revenue is the product $(2x) \cdot (100x^2) = 200x^3$ euros.