Monomials: Adding, Subtracting, Multiplying, Powers

Front

What is a monomial?

Back

A monomial is a polynomial with only one term, which can be a number, a variable, or a product of numbers and variables raised to non-negative integer powers.

Front

How do you add monomials?

Back

To add monomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

How do you subtract monomials?

Back

To subtract monomials, subtract the coefficients of like terms while keeping the variable part the same.

Front

What is the product of two monomials?

Back

The product of two monomials is found by multiplying their coefficients and adding the exponents of like bases.

Front

What is the power of a monomial?

Back

The power of a monomial is found by raising the coefficient to the given power and multiplying the exponents of the variables by that power.

Front

Calculate the volume of a cube with side length (-2c^3).

Back

Volume = side^3 = (-2c^3)^3 = -8c^9.

Front

What is the total area of two sections with areas 10m^2n and 7mn^2?

Back

Total area = 10m^2n + 7mn^2 = 9m^2n + 7mn^2.

Front

Simplify (3x^4y^5)^2.

Back

(3x^4y^5)^2 = 9x^8y^{10}.

Front

Find the product of (2a^3) and (3b^2).

Back

Product = 2a^3 * 3b^2 = 6a^3b^2.

Front

Calculate the total number of plants from (2a^2b^4z) and (6a^3b^2z^5).

Back

Total = 2a^2b^4z + 6a^3b^2z^5 = 12a^5b^6z^6.