Answer:
Sum:
1. 11p²+7p-12
2. 2x²+5z²-z+6
3. 3a²b-7ab²+4ab
4. 2d²+5cd+10c
5. -5x³+y³-4x²y+2y²
Difference:
1. 17p²+7p-12
2. 2x²+5x²+5z
3. 9a²b-7ab²-8ab
4. -7d²+5cd-4c
5. -7x³+y³-6x²y+6xy²-2y²
Step-by-step explanation:
1.) 14p² and -3p²+7p-12
Sum: 14p² + ( -3p²+7p-12)
=11p²+7p-12
Difference: 14p² - (-3p²+7p-12)
=17p²+7p-12
2.) (5z²+2z+3) and (-3z+2x²+3)
Sum: (5z²+2z+3) + (-3z+2x²+3)
=2x²+5z²-z+6
Difference: (5z²+2z+3) - (-3z+2x²+3)
=2x²+5x²+5z
3.) (9ab-11ab+6a²b) and (6ab-7ab²-3a²b)
Sum: (9ab-11ab+6a²b) + (6ab-7ab²-3a²b)
- 9ab+6ab-11ab=4ab, 6a²b+(-3a²b)= 3a²b =3a²b-7ab²+4ab
Difference: (9ab-11ab+6a²b) - (6ab-7ab²-3a²b)
- 9ab-6ab-11ab= -8ab, 6a²b-(-3a²b)= 9a²b
=9a²b-7ab²-8ab
4.) (3c+5cd-3d²) and (7c+5d²)
Sum: (3c+5cd-3d²) + (7c+5d²)
=2d²+5cd+10c
Difference: (3c+5cd-3d²) - (7c+5d²)
- 3c-7c= -4c, -3d²-5d²= -7d²
=-7d²+5cd-4c
5.) (x³-5x²y+3xy²+y³) and (-6x³+x²y-3xy²+2y²)
Sum:
(x³-5x²y+3xy²+y³) + (-6x³+x²y-3xy²+2y²)
- x³+(-6x³)=-5x³, -5x²y+x²y=-4x²y, 3xy²+(-3xy²)=0
=-5x³+y³-4x²y+2y²
Difference:
(x³-5x²y+3xy²+y³) - (-6x³+x²y-3xy²+2y²)
- x³-(-6x³)=7x³, -5x²y-x²y= -6x²y, 3xy²-(-3xy²)=6xy²
=-7x³+y³-6x²y+6xy²-2y²
