Mastering Polynomial Multiplication Techniques

This video tutorial covers the multiplication of polynomials by monomials, focusing on the application of exponent rules and the distributive property. It explains how to handle different variables, simplify expressions, and solve equations involving monomial distribution. The lesson includes examples and encourages students to practice independently.

What is the result of multiplying 2x by 7x^2?

• 9x^2

• 14x^3

• 9x^3

• 14x^2

When distributing a monomial across a polynomial, what should you do with the exponents of like variables?

• Divide them

• Add them

• Multiply them

• Subtract them

If you multiply 4x by 7x^2, what is the coefficient of the resulting term?

• 21

• 11

• 28

• 14

When distributing 4xy across a trinomial, what should be the order of the variables in the resulting terms?

• Order of appearance

• Random order

• Reverse alphabetical order

• Alphabetical order

What is the result of distributing -7h^2x across 7h^2x^2?

• -49h^4x^3

• -49h^2x^4

• 49h^4x^3

• 49h^2x^4

After distributing and combining like terms, what is the simplified form of 18n^4 - 27n^4?

• -45n^4

• 9n^4

• -9n^4

• 45n^4

What is the simplified form of 8m^4 - 16m^2 + 56m^4 - 77m^2 + 21m?

• 64m^4 - 93m^2 + 21m

• 64m^4 - 93m^2 - 21m

• 64m^4 + 93m^2 + 21m

• 64m^4 + 93m^2 - 21m

What is the result of distributing -8w across w?

• -8w^2

• 8w^2

• -8w

• 8w

In the equation -8w^2 + 18w = -8w^2 + 27w + 18, what is the next step after combining like terms?

• Subtract 18 from both sides

• Add 18 to both sides

• Subtract 27w from both sides

• Add 27w to both sides

What is the final value of w in the equation -9w = 18?

• -3

• 2

• -2

• 3