1. 21y² + 4y-1
2. 2x³ + 2x² + 11x - 12
3. m (m + 7m)
4. 7z³ + 2z² + - 2z + 1
5. 2a² + 5a + -9
6. 2x² + 3x + -8
7. -9z² -4z + 2
8. 6x³ -7x² - 6x -12
9. 3x² - 2x + 2
10. -3s² - 10s - 3
Solution
1. (12y² + 17y- 4) + (9y² - 13y + 3)
= (12y² + 17y- 4) + (9y² - 13y + 3)
= 12y² + 9y²+ 17y - 13y - 4 + 3
Answer: 21y² + 4y-1
2. (2x³ + 7x2 +x) + (2x² - 4x - 12)=
=(2x³ + 14x +x) + (2x² - 4x - 12)
=2x³ + 14x +x + 2x² - 4x - 12
= 2x³ + (14x +x - 4x) 2x² - 12
=2x³ + (14 +1 - 4) 2x² - 12
=2x³ + 11x + 2x² - 12
=2x³ + 2x² + 11x - 12
Answer: 2x³ + 2x² + 11x - 12
3. (-3m² + m) + (4m² + 6m)
=(-3m² + m) + (4m² + 6m)
= -m ( 3m - 1) + (4m² + 6m)
= (-m ( 3m - 1) - (4m² + 6m))
= - ( 3m² - m - 4m² - 6m)
= - ( -m² - 7m)
= - ( -m (m + 7m))
= m (m +7m)
Answer: m (m + 7m)
4. (7z³ + 4z - 1) + (2z² - 6z + 2)
= (7z³ + 4z - 1) + (2z² - 6z + 2)
= 7z³ + 4z - 1 + 2z² - 6z + 2
= 7z³ + (4z - 6z) + (-1 + 2) + 2z²
= 7z³ + (4 - 6) x z + (-1 + 2) + 2z²
= 7z³ + 2z + (-1 + 2) + 2z²
= 7z³ + 2z + -1 + 2z²
= 7z³ + 2z² + - 2z + 1
Answer: 7z³ + 2z² + - 2z + 1
5. (3a² + 2a - 2) - (a² - 3a+7)
= (3a² + 2a - 2) - (a² - 3a+7)
= (3a² - a² ) + (2a + 3a) + ( -2 - 7 )
= (3 - 1 ) a² + (2a + 3a) + ( -2 - 7 )
= (3 - 1 ) a² + (2 + 3) x a + ( -2 - 7 )
= 2a² + (2 + 3) x a + ( -2 - 7 )
= 2a² + 5a + ( -2 - 7 )
= 2a² + 5a + -9
Answer: 2a² + 5a + -9
6. (5x² - 2x -1 ) - (3x² - 5x + 7)
=(5x² - 2x -1 ) - (3x² - 5x + 7)
= 5x² - 2x -1 - 3x² - 5x + 7
= (5x² - 3x²) + ( -2x + 5x) + ( -1 - 7)
= (5 - 3 )x² + ( -2x + 5x) + ( -1 - 7)
= (5 - 3 )x² + (-2 + 5) x x + ( -1 - 7)
= 2x² + (-2 + 5) x x + ( -1 - 7)
= 2x² + 3x + ( -1 - 7)
= 2x² + 3x + -8
Answer: 2x² + 3x + -8
7. -(3z² + 4z) - (6z² - 2)
= -3z² + 4z - 6z² - 2
= (-3z² - 6z²) - 4z + 2
= (-3z² - 6z²) - 4z + 2
= (-3 - 6) z² - 4z + 2
= -9z² -4z + 2
Answer: -9z² -4z + 2
8. (6x³ - 4x² + x-9) - (3x² + 7x + 3)
= (6x³ - 4x² + x-9) - (3x² + 7x + 3)
= 6x³ - 4x² + x-9 - 3x² + 7x + 3
= 6x³ + (-4x² - 3x²) + ( x - 7x ) + (-9 - 3)
= 6x³ + (-4 - 3)x² + ( x - 7x ) + (-9 - 3)
= 6x³ -7x² + ( 1 - 7 ) x + (-9 - 3)
= 6x³ -7x² + 6x + (-9 - 3)
= 6x³ -7x² - 6x -12
Answer: 6x³ -7x² - 6x -12
9. (2x² + 1) + (x² - 2x + 1)
= (2x² + 1) + (x² - 2x + 1)
= 2x² + 1 + x² - 2x + 1
= (2x² + x²) + ( 1 + 1) -2x
= (2 + 1 ) x² + ( 1 + 1) -2x
= 3x² + ( 1 + 1) -2x
= 3x² + 2 -2x
= 3x² - 2x + 2
Answer: 3x² - 2x + 2
10. (-s² - 3) - (2s² + 10s)
= (-s² - 3) - (2s² + 10s)
= -s² - 3 - 2s² - 10s
= (-s²-2s²) - 3 - 10s
= (-1- 2) s² -3 - 10s
= -3s² - 3 - 10s
= -3s² - 10s - 3
Answer: -3s² - 10s - 3
