Review on Operations with Monomials

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 multiply two monomials?

Back

To multiply two monomials, multiply their coefficients and add their exponents for like bases. For example, (3x^2)(4x^3) = 12x^(2+3) = 12x^5.

Front

What is the product of (-3c^2) and (-10c^7)?

Back

30c^9.

Front

How do you find the area of a square given one side?

Back

The area of a square is found by squaring the length of one side. If one side is 8x^3, the area is (8x^3)^2 = 64x^6.

Front

What is the formula for dividing monomials?

Back

To divide monomials, divide their coefficients and subtract the exponents of like bases. For example, \frac{32x^6}{4x^2} = 8x^(6-2) = 8x^4.

Front

What is the result of multiplying 2xy by 3x^2y^3?

Back

6x^3y^4.

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form by combining like terms and performing operations.

Front

What is the result of simplifying (-x^2y^3) - (-2x^2y^3)?

Back

x^2y^3.

Front

What is a coefficient in a monomial?

Back

A coefficient is a numerical factor in a monomial. For example, in 5x^2, 5 is the coefficient.

Front

What is the degree of a monomial?

Back

The degree of a monomial is the sum of the exponents of its variables. For example, the degree of 4x^3y^2 is 3 + 2 = 5.