To solve the problem, we need to multiply the polynomials in each square and use the results to navigate through the maze. Let's go step by step.
Step 1: Start Here!
The starting point is:
\[ 4x^3(2x^5 - 10) \]
#### Multiply:
\[ 4x^3 \cdot 2x^5 = 8x^8 \]
\[ 4x^3 \cdot (-10) = -40x^3 \]
So, the result is:
\[ 8x^8 - 40x^3 \]
This matches the arrow pointing to the next square:
\[ (x - 5)(x + 8) \]
Step 2: Next Square
Multiply:
\[ (x - 5)(x + 8) \]
Use the distributive property (FOIL method):
\[ x \cdot x + x \cdot 8 - 5 \cdot x - 5 \cdot 8 \]
\[ x^2 + 8x - 5x - 40 \]
\[ x^2 + 3x - 40 \]
This matches the arrow pointing to the next square:
\[ 5xy(x + 4y) \]
Step 3: Next Square
Multiply:
\[ 5xy(x + 4y) \]
Distribute \( 5xy \):
\[ 5xy \cdot x + 5xy \cdot 4y \]
\[ 5x^2y + 20xy^2 \]
This matches the arrow pointing to the next square:
\[ (9x)(2x - 1) \]
Step 4: Next Square
Multiply:
\[ (9x)(2x - 1) \]
Distribute \( 9x \):
\[ 9x \cdot 2x + 9x \cdot (-1) \]
\[ 18x^2 - 9x \]
This matches the arrow pointing to the "FINISHED!" square.
Final Answer:
The path through the maze is:
\[ 4x^3(2x^5 - 10) \rightarrow (x - 5)(x + 8) \rightarrow 5xy(x + 4y) \rightarrow (9x)(2x - 1) \]
The final answer is:
\[
\boxed{18x^2 - 9x}
\]
Parent Tip: Review the logic above to help your child master the concept of polynomial multiplication worksheet.
