(i) 103 x 107 = (100 + 3)(100 + 7) = (100)² + (3 + 7)100 + 3 x 7 [∵ (x + a)(x + b) = x² + (a + b)x + ab ] = 10000 + 1000 + 21 = 11021 See this for video explanation of this answer✌😁
(i) 103 x 107
= (100 + 3)(100 + 7)
= (100)² + (3 + 7)100 + 3 x 7 [∵ (x + a)(x + b) = x² + (a + b)x + ab ]
= 10000 + 1000 + 21 = 11021
Evaluate the following products without multiplying directly: 103 × 107
(i) 103 x 107 = (100 + 3)(100 + 7) = (100)² + (3 + 7)100 + 3 x 7 [∵ (x + a)(x + b) = x² + (a + b)x + ab ] = 10000 + 1000 + 21 = 11021 See this for video explanation of this answer✌😁
(i) 103 x 107
= (100 + 3)(100 + 7)
= (100)² + (3 + 7)100 + 3 x 7 [∵ (x + a)(x + b) = x² + (a + b)x + ab ]
= 10000 + 1000 + 21 = 11021
See this for video explanation of this answer✌😁
See lessEvaluate the following products without multiplying directly: 95 × 96
(ii) 95 x 96 (100 - 5)(100 - 4) = (100)² + (-5 - 4)100 +(-5) x (-4) [∵ (x + a)(x + b) = x² + (a + b)x + ab ] = 10000 - 900 + 20 = 9120
(ii) 95 x 96
See less(100 – 5)(100 – 4)
= (100)² + (-5 – 4)100 +(-5) x (-4) [∵ (x + a)(x + b) = x² + (a + b)x + ab ]
= 10000 – 900 + 20 = 9120
Evaluate the following products without multiplying directly: 104 × 96
(iii) 104 x 96 (100 + 4)(100 - 4) = (100)² - (4)² [∵ (a + b)(a - b) = a² - b²] = 10000 - 16 = 9984
(iii) 104 x 96
See less(100 + 4)(100 – 4)
= (100)² – (4)² [∵ (a + b)(a – b) = a² – b²]
= 10000 – 16 = 9984
Factorise the following using appropriate identities: 9x² + 6xy + y²
(i) 9x² + 6xy + y² = (3x)² + 2 × 3x × y + y² = (3x + y)² [∵ a² + 2ab + b² = (a + b)]²
(i) 9x² + 6xy + y²
See less= (3x)² + 2 × 3x × y + y²
= (3x + y)² [∵ a² + 2ab + b² = (a + b)]²
Factorise the following using appropriate identities: 4y² – 4y + 1
(ii) 4y² - 4y + 1 = (2y)² - 2 × 2y × 1 + 1² = (2y - 1)² [∵ a² - 2ab + b² = (a - b)²]
(ii) 4y² – 4y + 1
See less= (2y)² – 2 × 2y × 1 + 1²
= (2y – 1)² [∵ a² – 2ab + b² = (a – b)²]