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. \( \left(9 r^{2}-6 r+1\right)-\left(-6 r^{2}+2 r-1\right) \)

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: \( 15r^2-8r+2 \)