GSEB Solutions for Class 8 Mathematics – Expansion (English Medium)
GSEB SolutionsMathsScience
Exercise
Solution 1:
- 2a(-3a2)
= -6a3 - (-4ab)(6a2b)
= -24a3b2 - (2m)(3m + n)
= (2m × 3m) + (2m × n)= 6m2 + 2mn - (-4n)(6n + 5m)
= (-4n × 6n) + (-4n × 5m)= -24n2 – 20mn - (5a + 3b)(6a – 2b)
= 5a(6a – 2b) + 3b(6a – 2b)= 30a2 – 10ab + 18ab – 6b2= 30a2 + 8ab – 6b2 - (2x + 3y)(6x – 2y)
= 2x(6x – 2y) + 3y(6x – 2y)= 12x2 – 4xy + 18xy – 6y2= 12x2 + 14xy – 6y2 - (6xy + 1)(2xy – 3)
= 6xy(2xy – 3) + 1(2xy – 3)= 12x2y2 – 18xy + 2xy – 3= 12x2y2 – 16xy – 3 - (a – 2b)(2a – b)
= a(2a – b) – 2b(2a – b)= 2a2 – ab – 4ab + 2b2= 2a2 – 5ab + 2b2
Solution 2:
- (a + 5)2= (a)2 + 2(a)(5) + (5)2
= a2 + 10a + 25 - (m – 7)2= (m)2 – 2(m)(7) + (7)2
= m2 – 14m + 49 - (3m + 2n)2= (3m)2 + 2(3m)(2n) + (2n)2
= 9m2 + 12mn + 4n2 - (4xy – 3)2= (4xy)2 – 2(4xy)(3) + (3)2
= 16x2y2 – 24xy + 9 - (5ab + 3c)2= (5ab)2 + 2(5ab)(3c) + (3c)2
= 25a2b2 + 30abc + 9c2 - (4b2 + 3)2= (4b2)2 + 2(4b2)(3) + (3)2
= 16b4 + 24b2 + 9 - (2x – 7)2= (2x)2 – 2(2x)(7) + (7)2
= 4x2 – 28x + 49 - (5 – 3mn)2= (5)2 – 2(5)(3mn) + (3mn)2
= 25 – 30mn + 9m2n2
Solution 3:
- (x – 7)(x + 7)= (x)2 – (7)2= x2 – 49
- (2a + 3b)(2a – 3b)= (2a)2 – (3b)2= 4a2 – 9b2
- (2m + 5)(2m – 5)= (2m)2 – (5)2= 4m2 – 25
- (2mn + 3)(2mn – 3)= (2mn)2 – (3)2= 4m2n2 – 9
Solution 4:
- (a + 3)(a + 2)
= (a)2 + (3 + 2)(a) + (3)(2)= a2 + 5a + 6 - (m – 2)(m – 5)
= (m)2 + (-2 – 5)(m) + (-2)( -5)= m2 – 7m + 10 - (x – 9)(x + 2)
= (x)2 + (-9 + 2)(x) + (-9)(2)= x2 + (-7)(x) – 18= x2 – 7x – 18 - (x + 6y)(x – 2y)
= (x)2 + (6y – 2y)(x) + (6y)(-2y)= x2 + (4y)(x) – 12y2= x2 + 4xy – 12y2 - (5x – 2y)(5x – 4y)
= (5x)2 + (-2y – 4y)(5x) + (-2y)( -4y)= 25x2 + (-6y)(5x) + 8y2= 25x2 – 30xy + 8y2 - (2m + 3n)(2m + 5n)
= (2m)2 + (3n + 5n)(2m) + (3n)(5n)= 4m2 + (8n)(2m) + 15n2= 4m2 + 16mn + 15n2 - (xy – 7)(xy + 4)
= (xy)2 + (-7 + 4)(xy) + (-7)(4)= x2y2 – 3xy – 28 - (x2 – 5)(x2 + 3)
= (x2)2 + (-5 + 3)(x2) + (-5)(3)= x4 – 2x2 – 15
Solution 5:
- 622= (60 + 2)2
= (60)2 + 2(60)(2) + (2)2= 3600 + 240 + 4= 3844 - 572
= (60 – 3)2= (60)2 – 2(60)(3) + (3)2= 3600 – 360 + 9= 3249 - 43 × 37
= (40 + 3)(40 – 3)= (40)2 – (3)2= 1600 – 9= 1591 - 97 × 103
= (100 – 3)(100 + 3)= (100)2 – (3)2= 10000 – 9= 9991 - 16 × 22
= (20 – 4)(20 + 2)= (20)2 + (-4 + 2)(20) + (-4) (2)= 400 + (-2)(20) – 8= 400 – 40 – 8= 352
Practice 1
Solution 1:
Solution 2:
- 2a(3x + 5y)
= (2a × 3x) + (2a × 5y)= 6ax + 10ay - 3x2(5x – 4y)
= (3x2 × 5x) – (3x2 × 4y)= 15x3 – 12x2y - 5a(6a + 3b)
= (5a × 6a) + (5a × 3b)= 30a2 + 15ab - (-6y)(5x – 7y2)
= [(-6y) × (5x)]-[(-6y) × (7y2)]= -30xy + 42y3 - (-10a)(5a2 + b)
= [(-10a) × (5a2)] + [(-10a) × (b)]= -50a3 – 10ab - (-3ab)(2a + 3b)
= [(-3ab) × (2a)] + [(-3ab) × (3b)]= -6a2b – 9ab2 - (6x3y3 – 1)(-2x2)
= [(6x3y3) × (-2x2) – [(1) × (-2x2)]= -12x5y3 + 2x2 - 2ab(3ab – 1)
= (2ab × 3ab) – (2ab × 1)= 6a2b2 – 2ab
Solution 3:
- (2x + y)(a + 3b)
= 2x(a + 3b) + y(a + 3b)= 2xa + 6xb + ya + 3yb - (5x – 3)(2a + 5)
= 5x(2a + 5) – 3(2a + 5)= 10ax + 25x – 6a – 15 - (x – 2)(x2 + 3)
= x(x2 + 3) – 2(x2 + 3)= x3 + 3x – 2x2 – 6 - (5x2 + 3)(2x2 + 5)
= 5x2(2x2 + 5) + 3(2x2 + 5)= 10x4 + 25x2 + 6x2 + 15= 10x4 + 31x2 + 15 - (x – 3)(x – 7)
= x(x – 7) – 3(x – 7)= x2 – 7x – 3x + 21= x2 – 10x + 21 - (2m2 + 5)(3m + 1)
= 2m2(3m + 1) + 5(3m + 1)= 6m3 + 2m2 + 15m + 5 - (3x + 5)(2x – 4)
= 3x(2x – 4) + 5(2x – 4)= 6x2 – 12x + 10x – 20= 6x2 – 2x – 20 - (x – 3a)(4x + 5a)
= x(4x + 5a) – 3a(4x + 5a)= 4x2 + 5xa – 12xa – 15a2= 4x2 – 7xa – 15a2
Practice 2
Solution 1:
- (x – y)2 = x2 – 2xy + y2
- (a + 7)2 = a2 + 14a + 49
- (2m – n)2 = 4m2 – 4mn + n2
- (x + 1)2 = x2 + 2x + 1
- (2a – 3)2 = 4a2 – 12a + 9
- (m + 2)2 = m2 + 4m + 4
Solution 2:
- (x + 7)2= (x)2 + 2(x)(7) + (7)2
= x2 + 14x + 49 - (m – 4)2= (m)2 – 2(m)(4) + (4)2
= m2 – 8m + 16 - (x + 3y)2= (x)2 + 2(x)(3y) + (3y)2
= x2 + 6xy + 9y2 - (8x + 5y)2= (8x)2 + 2(8x)(5y) + (5y)2
= 64x2 + 80xy + 25y2 - (2a – 3b)2= (2a)2 – 2(2a)(3b) + (3b)2
= 4a2 – 12ab + 9b2 - (4ab – 3xy)2= (4ab)2 – 2(4ab)(3xy) + (3xy)2
= 16a2b2 – 24abxy + 9x2y2 - (3xy – 7)2= (3xy)2 – 2(3xy)(7) + (7)2
= 9x2y2 – 42xy + 49 - (2xy – 3z)2= (2xy)2 – 2(2xy)(3z) + (3z)2
= 4x2y2 – 12xyz + 9z2
Solution 3:
- (43)2= (40 + 3)2= (40)2 + 2(40)(3) + (3)2
= 1600 + 240 + 9= 1849 - (82)2= (90 – 8)2= (90)2 – 2(90)(8) + (8)2
= 8100 – 1440 + 64= 6724 - (67)2= (60 + 7)2= (60)2 + 2(60)(7) + (7)2
= 3600 + 840 + 49= 4489 - (48)2= (50 – 2)2= (50)2 – 2(50)(2) + (2)2
= 2500 – 200 + 4= 2304
Practice 3
Solution 1:
Solution 2:
- (4x + 1)(4x – 1)= (4x)2 – (1)2= 16x2 – 1
- (3x – 7y)(3x + 7y)= (3x)2 – (7y)2= 9x2 – 49y2
- (6 – x)(6 + x)= (6)2 – (x)2= 36 – x2
- (a + 8b)(a – 8b)= (a)2 – (8b)2= a2 – 64b2
- (11 + 3xy)(11 – 3xy)= (11)2 – (3xy)2= 121 – 9x2y2
- (2mn + 5)(2mn – 5)= (2mn)2 – (5)2= 4m2n2 – 25
Solution 3:
- 41 × 39= (40 + 1)(40 – 1)= (40)2 – (1)2= 1600 – 1= 1599
- 56 × 64= (60 – 4)(60 + 4)= (60)2 – (4)2= 3600 – 16= 3584
- 73 × 67= (70 + 3)(70 – 3)= (70)2 – (3)2= 4900 – 9= 4891
- 33 × 27= (30 + 3)(30 – 3)= (30)2 – (3)2= 900 – 9= 891
Practice 4
Solution 1:
- (y + 2)(y + 4)= y2 + 6y + 8
- = (y)2 + (2 + 4)(y) + (2)(4)
- (m + 6)(m – 2)= m2 + 4m – 12
- = (m)2 + (6 – 2)(m) + (6)( -2)
- (2a – 5)(2a + 3)= 4a2 + (-2)(2a) – 15
- = 4a2 – 4a – 15
- = (2a)2 + (-5 + 3)(2a) + (-5)(3)
- (4x – 2y)(4x + y)= 16x2 + (-y)(4x) + (-2y2)
- = 16x2 – 4xy – 2y2
- = (4x)2 + (-2y + y)(4x) + (-2y)(y)
- (a – 3b)(a + 2b)= a2 + (-b)(a) – 6b2
- = a2 – ab – 6b2
- = (a)2 + (-3b + 2b)(a) + (-3b)(2b)
- (5ab – 3)(5ab + 2)= 25a2b2 + (-1)(5ab) – 6
- = 25a2b2 – 5ab – 6
- = (5ab)2 + (-3 + 2)(5ab) + (-3)(2)
- (6x + 3)(6x + 5)= 36x2 + (8)(6x) + 15
- = 36x2 + 48x + 15
- = (6x)2 + (3 + 5)(6x) + (3)(5)
- (7a + 4)(7a + 3)= 49a2 + (7)(7a) + 12
- = 49a2 + 49a + 12
- = (7a)2 + (4 + 3)(7a) + (4)(3)
Solution 2:
- 43 × 42= (40 + 3)(40 + 2)= (40)2 + (3 + 2)(40) + (3)(2)= 1600 + (5)(40) + 6
= 1600 + 200 + 6= 1806 - 68 × 73= (70 – 2)(70 + 3)= (70)2 + (-2 + 3)(70) + (-2)(3)= 4900 + (1)(70) – 6
= 4900 + 70 – 6= 4964 - 52 × 51= (50 + 2)(50 + 1)= (50)2 + (2 + 1)(50) + (2)(1)= 2500 + (3)(50) + 2
= 2500 + 150 + 2= 2652 - 24 × 19= (20 + 4)(20 – 1)= (20)2 + (4 – 1)(20) + (4)( -1)= 400 + (3)(20) – 4
= 400 + 60 – 4= 456 - 23 × 18= (20 + 3)(20 – 2)= (20)2 + (3 – 2)(20) + (3)( -2)= 400 + (1)(20) – 6
= 400 + 20 – 6= 414 - 27 × 32= (30 – 3)(30 + 2)= (30)2 + (-3 + 2)(30) + (-3)(2)= 900 + (-1)(30) – 6
= 900 – 30 – 6= 864