GSEB Solutions for Class 7 Mathematics – Polynomials (English Medium)
GSEB SolutionsMathsScience
Exercise
Solution 1:
6x + 4x
= (6 + 4)x
= 10x
Solution 2:
-8x – 2x
= (-8 – 2)x
= -10x
Solution 3:
25x2 – 6x2
= (25 – 6)x2
= 19x2
Solution 4:
8x3 – (-2x3)
= 8x3 + 2x3
= (8 + 2)x3
= 10x3
Solution 5:
5x2 + 3y – 2x2
= 5x2 – 2x2 + 3y
= (5 – 2)x2 + 3y
= 3x2 + 3y
Solution 6:
6x + (5 – 3x)
= 6x + 5 – 3x
= 6x – 3x + 5
= 3x + 5
Solution 7:
12m2 – 9m + 5m
= 12m2 + (-9 + 5)m
= 12m2 – 4m
Solution 8:
2x2 + 3x – 5 + 2x – 4
= 2x2 + 3x + 2x – 5 – 4
= 2x2 + (3 + 2)x – 9
= 2x2 + 5x – 9
Solution 9:
12m2 – m + 5m + 4m2 + 7m – 10
= 12m2 + 4m2 – m + 5m + 7m – 10
= (12 + 4)m2 + (-1 + 5 + 7)m – 10
= 16m2 + 11m – 10
Solution 10:
(5x2 + 3) – (2x2 – 4x – 7)
= 5x2 + 3 – 2x2 + 4x + 7
= 5x2 – 2x2 + 4x + 3 + 7
= (5 – 2)x2 + 4x + 10
= 3x2 + 4x + 10
Solution 11:
(9 – 3y) + (x2 + 5y – 6)
= 9 – 3y + x2 + 5y – 6
= x2 – 3y + 5y + 9 – 6
= x2 + (-3 + 5)y + 3
= x2 + 2y + 3
Solution 12:
(15 + 5x2 – 10x) + (4x – 2x2 – 5)
= 15 + 5x2 – 10x + 4x – 2x2 – 5
= 5x2 – 2x2 – 10x + 4x + 15 – 5
= (5 – 2)x2 + (-10 + 4)x + 10
= 3x2 – 6x + 10
Solution 13:
(10 – 3x2 + 4x) + (2x2 – 8x – 2)
= 10 – 3x2 + 4x + 2x2 – 8x – 2
= -3x2 + 2x2 + 4x – 8x + 10 – 2
= (-3 + 2)x2 + (4 – 8)x + 8
= -x2 – 4x + 8
Solution 14:
(9x2 – 3x – 6) – (4x + 5 – 2x2)
= 9x2 – 3x – 6 – 4x – 5 + 2x2
= 9x2 + 2x2 – 3x – 4x – 6 – 5
= (9 + 2)x2 + (-3 – 4)x – 11
= 11x2 – 7x – 11
Practice – 1
Solution 1:
Like terms have the same variable/s raised to the same power. Pairs of like terms are as follows:
- 2x2, 3x2
- 6x2y2, 9x2y2
- 5xy, 7xy
Solution 2:
- Like terms: 4xyz, 6xyz, 7xyz
Addition:
4xyz + 6xyz + 7xyz
=(4 + 6 + 7)xyz
= 17xyz - Like terms: 2x2y2, 3x2y2,9x2y2
Addition:
2x2y2 + 3x2y2 +9x2y2
=(2 + 3 + 9)x2y2
= 14 x2y2 - Like terms: 4x2, 18x2, 10x2
Addition:
4x2 + 18x2 + 10x2
= (4 + 18 + 10)x2
= 32x2
Solution 3:
(1) Perimeter of figure = Sum of the measures of all the sides
= 6a + a + 2a + 2a + a + 6a + 2a
= 20a
(2) The given figure is a rectangle.
Thus, perimeter = 2(length + breadth)
= 2(5b + 6b)
= 2(11b)
= 22b
Practice – 2
Solution 1:
Like terms have the same variable/s raised to the same power. Pairs of like terms are as follows:
- 2x2 and -3x2
-3y and 8y
6y2 and -4y2 - 3x2y and -5x2y
-xy and 5xy
5xy2 and -6xy2
4x3 and -8x3
Solution 2:
| Term | Like tem |
| (1) 3a2 | 5a2 |
| (2) -2y2z | -3y2z |
| (3) -7x | -5x |
| (4) -p2 | -9p2 |
| (5) 6abc | -2abc |
| (6) 11xy | 51xy |
Solution 3:
- 2x2 and -3x2
2x2 – (-3x2)
= 2x2 + 3x2
= (2 + 3)x2
= 5x2 - -3y and 8y
-3y – 8y
= -(3 + 8)y
=-11y - 6y2 and -4y2
6y2 – (-4y2)
= 6y2 + 4y2
= (6 + 4)y2
= 10y2 - 3x2y and -5x2y
3x2y – (-5x2y)
= 3x2y +5x2y
= (3 + 5)x2y
= 8x2y - -xy and 5xy
-xy – 5xy
= -(1 + 5)xy
= -6xy - 5xy2 and -6xy2
5xy2 – (-6xy2)
= 5xy2 + 6xy2
= (5 + 6)xy2
= 11xy2 - 4x3 and -8x3
4x3 – (-8x3)
= 4x3 + 8x3
= (4 + 8)x3
= 12x3
Solution 4:
- 4x2 – (-6xy2)
= 4x2 + 6xy2 - 6x3 – (-2x3)
= 6x3 + 2x3
= (6 + 2)x3
= 8x3 - 9xy – (5xy)
= (9 – 5)xy
= 4xy - -7x3 – (-8x3y)
= -7x3 + 8x3y
Practice – 3
Solution 1:
2x + (2x – 3)
= 2x + 2x – 3
= (2 + 2)x – 3
= 4x – 3
Solution 2:
(4m2 + 7) + 3m2
= 4m2 + 7 + 3m2
= (4 + 3)m2 + 7
= 7m2 + 7
Solution 3:
(-6m – 3) + 9
= -6m – 3 + 9
= -6m + 6
Solution 4:
(-5n) + (8n + 7)
= -5n + 8n + 7
= (-5n + 8n) + 7
= 3n + 7
Solution 5:
8x2 + 7 + (-8x2)
= 8x2 + 7 – 8x2
= (8 – 8)x2 + 7
= 0 + 7
= 7
Solution 6:
(3xy – 5) + 9xy
= (3 + 9)xy – 5
= 12xy – 5
Practice – 4
Solution 1:
Polynomials having two terms are called binomials.
- 2a + 3
- 5x – y
- 12m – 3
- 23 + p
- 4a – b
Solution 2:
- 3x + 2, 2x + 3
- 4x + 2, 7x – 5
- m + n, 3m + n
- 5p – 7, 2p – 4
- 2a + 2c, 3a – 2c
- 6a – 11, 3a – 12
- 3s + 2, s – 3
- 2x – 3, 4x – 5
- 3x + 1, x – 2
- 9a – 2b, 2a – 3b
Solution 3:
- 3x + 2 + 2x + 3
= 3x + 2x + 2 + 3
= (3 + 2)x + 5
= 5x + 5 - 4x + 2 + 7x – 5
= 4x + 7x – 5 + 2
= (4 + 7)x – 3
= 11x – 3 - m + n + 3m + n
= m + 3m + n + n
= 4m + 2n - 5p – 7 + 2p – 4
= 5p + 2p – 4 – 7
= (5 + 2)p – (4 + 7)
= 7p – 11 - 2a + 2c + 3a – 2c
= 2a + 3a + 2c – 2c
= (2 + 3)a + (2 – 2)c
= 5a + 0
= 5a - 6a – 11 + 3a – 12
= 6a + 3a – 11 – 12
= (6 + 3)a – (11 + 12)
= 9a – 23 - 3s + 2 + s – 3
= 3s + s + 2 – 3
= (3 + 1)s + 2 – 3
= 4s – 1 - 2x – 3 + 4x – 5
= 2x + 4x – 3 – 5
= (2 + 4)x – (3 + 5)
= 6x – 8 - 3x + 1 + x – 2
= 3x + x + 1 – 2
= (3 + 1)x – 1
= 4x – 1 - 9a – 2b + 2a – 3b
= 9a + 2a – 2b – 3b
= (9 + 2)a – (2 + 3)b
= 11a – 5b
Solution 4:
- (4xy + 5x2) + (6xy – 2x2)
= 4xy + 6xy + 5x2 – 2x2
= (4 + 6)xy + (5 – 2)x2
= 10xy + 3x2 - (3x + y) +(3x – 7y)
= 3x + 3x + y – 7y
= (3 + 3)x + (1 – 7)y
= 6x + (-6)y
= 6x – 6y - (3xy2 – 4) + (6xy2 + 8)
= 3xy2 + 6xy2 – 4 + 8
= (3 + 6)xy2 – 4 + 8
= 9xy2 + 4
Practice – 5
Solution 1:
(8p2 + 5) – (9p2 – 7)
= 8p2 + 5 – 9p2 + 7
= 8p2 – 9p2 + 5 + 7
= (8 – 9)p2 + 12
= -p2 + 12
Solution 2:
(3m + 4n) – (6n + 5m)
= 3m + 4n – 6n – 5m
= 3m – 5m + 4n – 6n
= (3 – 5)m + (4 – 6)n
= -2m – 2n
Solution 3:
(3p2) – (7p2 – 5)
= 3p2 – 7p2 + 5
= (3 – 7)p2 + 5
= -4p2 + 5
Solution 4:
(16a + 5b) – (-7b)
= 16a + 5b +7b
= 16a + (5 + 7)b
= 16a + 12b
Solution 5:
(-10b + 8) – (-3b)
= -10b + 8 + 3b
= -10b + 3b + 8
= (-10 + 3)b + 8
= -7b + 8
Solution 6:
(7x – 9) – 15
= 7x – 9 – 15
= 7x – 24
Solution 7:
(-3x – 5y) – (7x + 2y)
= -3x – 5y – 7x – 2y
= -3x – 7x – 5y – 2y
= (-3 – 7)x – (5 + 2)y
= -10x – 7y
Solution 8:
(abc + xy) – (3xy – 13abc)
= abc + xy – 3xy + 13abc
= abc + 13abc + xy – 3xy
= (1 + 13)abc + (1 – 3)xy
= 14abc – 2xy
Solution 9:
(7) – (a2 – 10)
= 7 – a2 + 10
= 7 + 10 – a2
= 17 – a2
Solution 10:
(15x2 + y2) – (10x2 – 2y2)
= 15x2 + y2 – 10x2 + 2y2
= 15x2 – 10x2 + y2 + 2y2
= (15 – 10)x2 + (1 + 2)y2
= 5x2 + 3y2
Practice – 6
Solution 1:
(2x + 3y + 5) + (-7x)
= 2x + 3y + 5 – 7x
= 2x – 7x + 3y + 5
= (2 – 7)x + 3y + 5
= -5x + 3y + 5
Solution 2:
(12m2 – 9m + 7) + (3m – 8)
= 12m2 – 9m + 7 + 3m – 8
= 12m2 – 9m + 3m + 7 – 8
= 12m2 + (-9 + 3)m + (7 – 8)
= 12m2 – 6m – 1
Solution 3:
(2x2 + 3x – 5) + (2x2 – 4)
= 2x2 + 3x – 5 + 2x2 – 4
= 2x2 + 2x2 + 3x – 5 – 4
= (2 + 2)x2 + 3x + (-5 – 4)
= 4x2 + 3x – 9
Solution 4:
(9b – 10a + 15) + (3a + b + 2)
= 9b – 10a + 15 + 3a + b + 2
= 9b + b – 10a + 3a + 15 + 2
= (9 + 1)b + (-10 + 3)a + 17
= 10b – 7a + 17
Solution 5:
(17a – 13b – 14) + (10a – 9b – 15)
= 17a – 13b – 14 + 10a – 9b – 15
= 17a + 10a – 13b – 9b – 14 – 15
= (17 + 10)a + (-13 – 9)b + (-14 – 15)
= 27a – 22b – 29
Solution 6:
(4p2 – 3p – 10) + (30)
= 4p2 – 3p – 10 + 30
= 4p2 – 3p + 20
Practice – 7
Solution 1:
(x2 + 2xy + y2) – (10x2)
= x2 + 2xy + y2 – 10x2
= x2 – 10x2 + 2xy + y2
= (1 – 10)x2 + 2xy + y2
= -9x2 + 2xy + y2
Solution 2:
(6a3 + 10b2 – 25ab) – (-25ab)
= 6a3 + 10b2 – 25ab + 25ab
= 6a3 + 10b2
Solution 3:
(a2 + b2 – 7ab) – (3b2)
= a2 + b2 – 7ab – 3b2
= a2 + b2 – 3b2 – 7ab
= a2 + (1 – 3)b2 – 7ab
= a2 – 2b2 – 7ab
Solution 4:
(10x2 + 6xy + y2) – (9x2 – y2)
= 10x2 + 6xy + y2 – 9x2 + y2
= 10x2 – 9x2 + 6xy + y2 + y2
= (10 – 9)x2 + 6xy + (1 + 1)y2
= x2 + 6xy + 2y2
Solution 5:
(3abc + 5bc – 6ac) – (-7abc – 9bc)
= 3abc + 5bc – 6ac + 7abc + 9bc
= 3abc + 7abc + 5bc + 9bc – 6ac
= (3 + 7)abc + (5 + 9)bc – 6ac
= 10abc + 14bc – 6ac
Solution 6:
(2x – 3y + 15) – (13y + 12)
= 2x – 3y + 15 – 13y – 12
= 2x – 3y – 13y + 15 – 12
= 2x + (-3 – 13)y + 3
= 2x – 16y + 3
Solution 7:
(-5xy – 8x – 9) – (7xy – 7x + 6)
= -5xy – 8x – 9 – 7xy + 7x – 6
= -5xy – 7xy – 8x + 7x – 9 – 6
= (-5 – 7)xy + (-8 + 7)x – 15
= -12xy – x – 15
Solution 8:
(a2 + b2 + 2ab) – (3a2 – 2ab + 5b2)
= a2 + b2 + 2ab – 3a2 + 2ab – 5b2
= a2 – 3a2 + b2 – 5b2 + 2ab + 2ab
= (1 – 3)a2 + (1 – 5)b2 + (2 + 2)ab
= -2a2 – 4b2 + 4ab
Solution 9:
(3x2 + 3x – 5) – (2x2 – 8x – 5)
= 3x2 + 3x – 5 – 2x2 + 8x + 5
= 3x2 – 2x2 + 3x + 8x – 5 + 5
= (3 – 2)x2 + (3 + 8)x + 0
= x2 + 11x
Solution 10:
(3x2 + 5xy – 9) – (x2 – 2xy + 5)
= 3x2 + 5xy – 9 – x2 + 2xy – 5
= 3x2 – x2 + 5xy + 2xy – 9 – 5
= (3 – 1)x2 + (5 + 2)xy – 14
= 2x2 + 7xy – 14
Solution 11:
(2x2 – x + 14) – (5x – 3x2 + 8)
= 2x2 – x + 14 – 5x + 3x2 – 8
= 2x2 + 3x2 – x – 5x + 14 – 8
= (2 + 3)x2+ (-1 – 5)x + 6
= 5x2 – 6x + 6
Solution 12:
(9x2 + 5x – 17) – (15 – 4x + 3x2)
= 9x2 + 5x – 17 – 15 + 4x – 3x2
= 9x2 – 3x2 + 5x + 4x – 17 – 15
= (9 – 3)x2 + (5 + 4)x – 32
= 6x2 + 9x – 32