1) Use algebra tiles to find $$ \left(-3 x^{2}+8\right)+\left(-7 x^{2}-10 x-8\right) $$

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UpStudy AI · Accepted Answer

To find the sum of the two polynomials $$(-3x^{2} + 8)$$ and $$(-7x^{2} - 10x - 8)$$ using algebra tiles, follow these steps:

### Step 1: Represent Each Polynomial with Algebra Tiles

1. **First Polynomial $$(-3x^{2} + 8)$$:**
   - **$$-3x^{2}$$:** Use 3 negatively marked $$x^{2}$$ tiles.
   - **$$+8$$:** Use 8 positively marked unit tiles.

2. **Second Polynomial $$(-7x^{2} - 10x - 8)$$:**
   - **$$-7x^{2}$$:** Use 7 negatively marked $$x^{2}$$ tiles.
   - **$$-10x$$:** Use 10 negatively marked $$x$$ tiles.
   - **$$-8$$:** Use 8 negatively marked unit tiles.

### Step 2: Combine Like Terms by Adding the Tiles

1. **Combine $$x^{2}$$ Tiles:**
   - $$-3x^{2}$$ (from the first polynomial) and $$-7x^{2}$$ (from the second polynomial) add up to $$-10x^{2}$$.

2. **Combine $$x$$ Tiles:**
   - Only $$-10x$$ exists in the second polynomial.

3. **Combine Unit Tiles:**
   - $$+8$$ (from the first polynomial) and $$-8$$ (from the second polynomial) cancel each other out, resulting in $$0$$.

### Step 3: Write the Final Simplified Expression

After combining all like terms, the simplified expression is:

$$
-10x^{2} - 10x
$$

### Conclusion

Using algebra tiles to visualize and combine like terms, the sum of $$(-3x^{2} + 8)$$ and $$(-7x^{2} - 10x - 8)$$ is:

$$
-10x^{2} - 10x
$$
The sum of $$(-3x^{2} + 8)$$ and $$(-7x^{2} - 10x - 8)$$ is $$-10x^{2} - 10x$$.

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