Multiplying Polynomials and Variables

This video tutorial explains how to multiply polynomials by demonstrating two examples. It covers the rules for multiplying coefficients and adding exponents, and provides step-by-step guidance on simplifying the expressions. The first example involves multiplying 2x^2 by 5xy^3, while the second example involves 25xy by 2xy^4z^2. The tutorial emphasizes the importance of understanding the properties of exponents and coefficients in polynomial multiplication.

What is the first step in multiplying polynomials?

• Subtract the exponents

• Add the exponents

• Multiply the coefficients

• Divide the coefficients

When a variable has no degree mentioned, what is its default power?

• Zero

• Two

• One

• Three

In the expression 2x^2 * 5xy^3, what is the result of multiplying the coefficients?

• 5

• 15

• 10

• 7

In the second example, what is the result of multiplying the coefficients 25 and 2?

• 50

• 30

• 45

• 60

How do you handle a variable that appears in only one term when multiplying polynomials?

• Multiply it by zero

• Subtract it from the other term

• Add it to the result as is

• Ignore it

What is the final power of y in the expression 25xy * 2xy^4?

• y^5

• y^6

• y^7

• y^8

In the expression 25xy * 2xy^4z^2, what happens to the z variable?

• It is ignored

• It is added to the result as z^2

• It is subtracted from the other term

• It is multiplied by zero

What is the final expression obtained from multiplying 25xy * 2xy^4z^2?

• 50x^3y^6z^2

• 50x^3y^7z^2

• 50x^2y^5z^2

• 50x^2y^7z^2