Multiply Polynomial by Monomial Game/Worksheet

Multiply Polynomial by Monomial Game/Worksheet
Welcome to the Multiply Polynomial by Monomial Challenge! This interactive web game challenges you to expand algebraic expressions. To expand an expression where a single term (a monomial) is multiplied by an expression with multiple terms (a polynomial), you use the Distributive Property. Scroll down the page for a more detailed explanation.

 

 

How to Play

1. Analyze the Challenge:
   Look at the active expression in the center of the board (for example,3x(2x + 5)).
   

2. Use the Scratchpad:
   Need to map out your steps? Use the Digital Scratchpad on the right side of the screen to calculate your individual terms before typing.
   

3. Submit Your Answer:
   Type your expanded expression into the text input box. Use the ^ symbol for exponents and leave out all spaces (e.g., 6x^2+15x). Click Verify Expansion or press Enter.
   

4. Review and Repeat:
   Check the instant feedback panel to see the full algebraic breakdown. Click Next Challenge to keep your win streak alive and earn more points.
   

How the Math Works
To expand an expression where a single term (a monomial) is multiplied by an expression with multiple terms (a polynomial), you use the Distributive Property.

When multiplying individual terms together, you follow two foundational algebraic rules:

Multiply the Coefficients:
Multiply the regular numbers in front of the variables.

Add the Exponents:
When multiplying identical variables, apply the Product Rule of Exponents:

x^a · x^b = x^a+b

Note: If a variable is written by itself (like x), it has an invisible exponent of 1 (x = x^a). If a term has no variable at all, it has an exponent value of 0 (x⁰ = 1).

Walkthrough Example
Let’s break down the game’s default problem:

3x(2x + 5)

Step 1: Distribute to Term 1
Multiply 3x by 2x.
Multiply the coefficients (3 · 2 = 6) and add the exponents (x¹ · x¹ = x¹⁺¹ = x²).

Result 1 = 6x²

Step 2: Distribute to Term 2
Multiply 3x by 5.
Multiply the coefficients (3 · 5 = 15). Since 5 doesn’t have a variable, the x stays exactly as it is (x¹).

Result 2 = 15x

Step 3: Combine the Terms
Put your results back together to get the final expanded expression:

6x² + 15x

Multiply Polynomial by Monomial

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