Add or subtract the polynomials. 5. $$ \left(-3 a^{3}+2 a^{2}-4\right)+\left(a^{3}-3 a^{2}-5 a+7\right) $$ $$ 6 .\left(7 x^{2} y^{2}-6 x^{3}+x y\right)-\left(5 x^{2} y^{2}-x^{3}+x y+x\right) $$

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Let's solve each problem step by step by combining like terms.

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**Problem 5**

Add the polynomials:
$$
(-3a^{3} + 2a^{2} - 4) + (a^{3} - 3a^{2} - 5a + 7)
$$

**Step-by-Step Solution:**

1. **Combine like terms:**
   - **$$a^3$$ terms:** $$-3a^3 + a^3 = -2a^3$$
   - **$$a^2$$ terms:** $$2a^2 - 3a^2 = -a^2$$
   - **$$a$$ terms:** $$-5a$$ (only one term)
   - **Constant terms:** $$-4 + 7 = 3$$

2. **Write the simplified expression:**
   $$
   -2a^3 - a^2 - 5a + 3
   $$

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**Problem 6**

Subtract the polynomials:
$$
(7x^{2}y^{2} - 6x^{3} + xy) - (5x^{2}y^{2} - x^{3} + xy + x)
$$

**Step-by-Step Solution:**

1. **Distribute the subtraction across the second polynomial:**
   $$
   7x^{2}y^{2} - 6x^{3} + xy - 5x^{2}y^{2} + x^{3} - xy - x
   $$

2. **Combine like terms:**
   - **$$x^3$$ terms:** $$-6x^3 + x^3 = -5x^3$$
   - **$$x^2y^2$$ terms:** $$7x^2y^2 - 5x^2y^2 = 2x^2y^2$$
   - **$$xy$$ terms:** $$xy - xy = 0$$ (they cancel out)
   - **Constant term:** $$-x$$

3. **Write the simplified expression:**
   $$
   -5x^3 + 2x^2y^2 - x
   $$

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**Final Answers:**

5. $$-2a^3 - a^2 - 5a + 3$$

6. $$-5x^3 + 2x^2 y^2 - x$$
The simplified results are: 5. $$-2a^3 - a^2 - 5a + 3$$ 6. $$-5x^3 + 2x^2 y^2 - x$$

Add or subtract the polynomials.
5.

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