Adding \& Subtracting Quadratic Expressions (B) Simplify each expression. 1. $$ \left(-3 w^{2}+5 w-2\right)+\left(-9 w^{2}+4 w+5\right) $$ 2. $$ \left(9 z^{2}+9 z+6\right)+\left(z^{2}+4 z+7\right) $$ 3. $$ \left(-5 g^{2}+9 g-3\right)+\left(2 g^{2}-6 g+3\right) $$ 4. $$ \left(3 q^{2}+6 q-2\right)-\left(-3 q^{2}-8 q+2\right) $$ 5. $$ \left(-4 z^{2}+4 z+7\right)-\left(-9 z^{2}+z-7\right) $$ 6. $$ \left(6 w^{2}+9 w+9\right)-\left(7 w^{2}+6 w+5\right) $$ 7. $$ \left(5 p^{2}-3 p+3\right)-\left(-3 p^{2}+5 p+7\right) $$ 8. $$ \left(2 q^{2}+8 q+5\right)-\left(-5 q^{2}+8\right) $$ 9. $$ \left(-2 t^{2}-t-2\right)-\left(8 t^{2}+6 t-3\right) $$ 10. $$ \left(9 r^{2}-6 r+1\right)-\left(-6 r^{2}+2 r-1\right) $$

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1. $$ \left(-3w^2+5w-2\right)+\left(-9w^2+4w+5\right) $$
   - Combine the $$ w^2 $$ terms: $$ -3w^2-9w^2=-12w^2 $$
   - Combine the $$ w $$ terms: $$ 5w+4w=9w $$
   - Combine the constants: $$-2+5=3$$
   - Final answer: $$ -12w^2+9w+3 $$

2. $$ \left(9z^2+9z+6\right)+\left(z^2+4z+7\right) $$
   - Combine the $$ z^2 $$ terms: $$ 9z^2+z^2=10z^2 $$
   - Combine the $$ z $$ terms: $$ 9z+4z=13z $$
   - Combine the constants: $$ 6+7=13 $$
   - Final answer: $$ 10z^2+13z+13 $$

3. $$ \left(-5g^2+9g-3\right)+\left(2g^2-6g+3\right) $$
   - Combine the $$ g^2 $$ terms: $$ -5g^2+2g^2=-3g^2 $$
   - Combine the $$ g $$ terms: $$ 9g-6g=3g $$
   - Combine the constants: $$ -3+3=0 $$
   - Final answer: $$ -3g^2+3g $$

4. $$ \left(3q^2+6q-2\right)-\left(-3q^2-8q+2\right) $$
   - Distribute the subtraction: $$ 3q^2+6q-2+3q^2+8q-2 $$
   - Combine the $$ q^2 $$ terms: $$ 3q^2+3q^2=6q^2 $$
   - Combine the $$ q $$ terms: $$ 6q+8q=14q $$
   - Combine the constants: $$ -2-2=-4 $$
   - Final answer: $$ 6q^2+14q-4 $$

5. $$ \left(-4z^2+4z+7\right)-\left(-9z^2+z-7\right) $$
   - Distribute the subtraction: $$ -4z^2+4z+7+9z^2-z+7 $$
   - Combine the $$ z^2 $$ terms: $$ -4z^2+9z^2=5z^2 $$
   - Combine the $$ z $$ terms: $$ 4z-z=3z $$
   - Combine the constants: $$ 7+7=14 $$
   - Final answer: $$ 5z^2+3z+14 $$

6. $$ \left(6w^2+9w+9\right)-\left(7w^2+6w+5\right) $$
   - Distribute the subtraction: $$ 6w^2+9w+9-7w^2-6w-5 $$
   - Combine the $$ w^2 $$ terms: $$ 6w^2-7w^2=-w^2 $$
   - Combine the $$ w $$ terms: $$ 9w-6w=3w $$
   - Combine the constants: $$ 9-5=4 $$
   - Final answer: $$ -w^2+3w+4 $$

7. $$ \left(5p^2-3p+3\right)-\left(-3p^2+5p+7\right) $$
   - Distribute the subtraction: $$ 5p^2-3p+3+3p^2-5p-7 $$
   - Combine the $$ p^2 $$ terms: $$ 5p^2+3p^2=8p^2 $$
   - Combine the $$ p $$ terms: $$ -3p-5p=-8p $$
   - Combine the constants: $$ 3-7=-4 $$
   - Final answer: $$ 8p^2-8p-4 $$

8. $$ \left(2q^2+8q+5\right)-\left(-5q^2+8\right) $$
   - Distribute the subtraction: $$ 2q^2+8q+5+5q^2-8 $$
   - Combine the $$ q^2 $$ terms: $$ 2q^2+5q^2=7q^2 $$
   - The $$ q $$ term remains: $$ 8q $$
   - Combine the constants: $$ 5-8=-3 $$
   - Final answer: $$ 7q^2+8q-3 $$

9. $$ \left(-2t^2-t-2\right)-\left(8t^2+6t-3\right) $$
   - Distribute the subtraction: $$ -2t^2-t-2-8t^2-6t+3 $$
   - Combine the $$ t^2 $$ terms: $$ -2t^2-8t^2=-10t^2 $$
   - Combine the $$ t $$ terms: $$ -t-6t=-7t $$
   - Combine the constants: $$ -2+3=1 $$
   - Final answer: $$ -10t^2-7t+1 $$

10. $$ \left(9r^2-6r+1\right)-\left(-6r^2+2r-1\right) $$
    - Distribute the subtraction: $$ 9r^2-6r+1+6r^2-2r+1 $$
    - Combine the $$ r^2 $$ terms: $$ 9r^2+6r^2=15r^2 $$
    - Combine the $$ r $$ terms: $$ -6r-2r=-8r $$
    - Combine the constants: $$ 1+1=2 $$
    - Final answer: $$ 15r^2-8r+2 $$
1. $$ -12w^2 + 9w + 3 $$ 2. $$ 10z^2 + 13z + 13 $$ 3. $$ -3g^2 + 3g $$ 4. $$ 6q^2 + 14q - 4 $$ 5. $$ 5z^2 + 3z + 14 $$ 6. $$ -w^2 + 3w + 4 $$ 7. $$ 8p^2 - 8p - 4 $$ 8. $$ 7q^2 + 8q - 3 $$ 9. $$ -10t^2 - 7t + 1 $$ 10. $$ 15r^2 - 8r + 2 $$

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