class 8:maths : Expansion formulae :All Practice Set

 Class 8:Maths : Expansion formulae :Practice Set 5.1Practice Set 5.1 QUE (1)   Expand.  (1) (a +2)(a – 1)                             (2) (m – 4)(m + 6) (3) (p + 8)(p -3)                             
(4) (13 + x)(13 – x) (5) (3x + 4y)(3x + 5y)                 (6) (9x – 5t)(9x + 3t)(7). (m+23)(m−73)(8). (x+1x)(x−1x)(9). (1y+4)(1y−9)ANSWER :(1). (a + 2)(a – 1)= a² + (2 – 1) a + 2 × (-1)..[∵ (x + A) (x + B) = x² + (A + B)x + AB]= a² + a – 2(2). (m – 4)(m + 6)= m² + (- 4 + 6) m + (-4) × 6…[∵ (x + a) (x + b) = x² + (a + b)x + ab]= m² + 2m – 24(3). (p + 8) (p – 3)= p² + (8 – 3) p + 8 x (-3)…[∵ (x + a) (x + b) = x² + (a + b)x + ab]= p² + 5p – 24(4). (13 + x) (13 – x)= (13)² + (x – x) 13 + x × (-x)…[∵ (x + a) (x + b) = x² + (a + b)x + ab]= 169 + 0 × 13 – x²= 169 – x².(5). (3x + 4y) (3x + 5y)= (3x)² + (4y + 5y) 3x + 4y × 5y…[∵ (x + a) (x + b) = x² + (a + b)x + ab]= 9x² + 9y × 3x + 20y²= 9x² + 27xy + 20y².(6). (9x – 5t) (9x + 3t)= (9x)² + [(-5t) + 3t] 9x + (-5t) × 3t…[∵ (x + a) (x + b) = x² + (a + b)x + ab]= 81x² + (-2t) × 9x – 15t²= 81x² – 18xt – 15t²(7)(8)(9). Class 8:Maths : Expansion formulae :Practice Set 5.2Question 1.Expand:(1). (k + 4)³(2). (7x + 8y)³(3). (7x + m)³(4). (52)³(5). (101)³(6). (x+1x)3(7). (2m+15)3(8). (5xy+y5x)3Solution:(1). Here, a = k and b = 4(k + 4)³ = (k)³ + 3(k)² (4) + 3(k)(4)² + (4)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= k³ + 12k² + 3(k)(16) + 64= k³ + 12k² + 48k + 64(2). Here, a = 7x and b = 8y(7x + 8y)³= (7x)³ + 3(7x)² (8y) + 3(7x) (8y)² + (8y)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= 343x³ + 3(49x²)(8y) + 3(7x)(64y²) + 512y³= 343x³ + 1176x²y + 1344xy² + 512y³(3). Here, a = 7 and b = m(7 + m)³ = (7)³ + 3(7)²(m) + 3(7)(m)² + (m)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= 343 + 3(49)(m) + 3(7)(m²) + m³= 343 + 147m + 21m² + m³(4). (52)³ = (50 + 3)³Here, a = 50 and b = 2(52)³ = (50)³ + 3(50)² (2) + 3(50)(2)² + (2)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= 125000 + 3(2500)(2) + 3(50)(4) + 8= 125000 + 15000 + 600 + 8=140608(5). (101)³ = (100 + 1)³Here, a = 100 and b = 1(101)³= (100)³ + 3(100)²(1) + 3(100)(1)² + (1)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= 1000000 + 3(10000) + 3(100) (1) + 1= 1000000 + 30000 + 300 + 1= 1030301(6). Here, a = x and b = 1x1x(7). Here, a = 2m and b = 15(8). Here, a = 5xy and b = y5x