Question

c) combine like terms and then draw algebra tiles to represent the simplified expression
-5y³ - 6y - 3 + 8 + 3y - 2y³
simplified expression:
drawing of simplified expression:

d) combine like terms and then draw algebra tiles to represent the simplified expression
8x + 3x - 9 + 4x² - 2x - 5 + 14
simplified expression:
drawing of simplified expression:

Explanation:

Step1: Group $y^2$ terms

$$\begin{align*} -5y^2 - 2y^2 &= (-5-2)y^2 \\ &= -7y^2 \end{align*}$$

Step2: Group $y$ terms

$$\begin{align*} -6y + 3y &= (-6+3)y \\ &= -3y \end{align*}$$

Step3: Group constant terms

$$\begin{align*} -3 + 8 &= 5 \end{align*}$$

Step4: Combine all simplified terms

$-7y^2 - 3y + 5$

Step5: Group $x^2$ terms

$4x^2$ (only one $x^2$ term)

Step6: Group $x$ terms

$$\begin{align*} 8x + 3x - 2x &= (8+3-2)x \\ &= 9x \end{align*}$$

Step7: Group constant terms

$$\begin{align*} -9 - 5 + 14 &= 0 \end{align*}$$

Step8: Combine all simplified terms

$4x^2 + 9x$

Answer:

For part c:

Simplified expression: $-7y^2 - 3y + 5$
Drawing of simplified expression:

• 7 negative $y^2$ tiles (large squares, shaded/colored to represent negative)
• 3 negative $y$ tiles (rectangles, shaded/colored to represent negative)
• 5 positive constant tiles (small squares, unshaded to represent positive)

For part d:

Simplified expression: $4x^2 + 9x$
Drawing of simplified expression:

• 4 positive $x^2$ tiles (large squares, unshaded to represent positive)
• 9 positive $x$ tiles (rectangles, unshaded to represent positive)

(No constant tiles needed since the constant sum is 0)