(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
Use suitable identities to find the following products: (y²+3/2) (y²-3/2)
(iv) (y² + 3/2)(y² - 3/2) = (y²)² - (3/2)² [∵ (a + b)(a - b) = a² - b²] = y⁴ - 9/4
(iv) (y² + 3/2)(y² – 3/2)
See less= (y²)² – (3/2)² [∵ (a + b)(a – b) = a² – b²]
= y⁴ – 9/4
Use suitable identities to find the following products: (3 – 2x) (3 + 2x)
(v) (3 - 2x)(3 + 2x) = (3)² - (2x)² [∵ (a + b)(a - b) = a² - b²] = 9 - 4x²
(v) (3 – 2x)(3 + 2x)
See less= (3)² – (2x)² [∵ (a + b)(a – b) = a² – b²]
= 9 – 4x²
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]
Factorise the following using appropriate identities: x²- y²/100
(iii) x² - y²/100 = x² - (y/100)² = (x + y/100)(x - y/100) [∵ a² - b² = (a + b)(a - b)]
(iii) x² – y²/100
See less= x² – (y/100)²
= (x + y/100)(x – y/100) [∵ a² – b² = (a + b)(a – b)]
Expand each of the following, using suitable identities: (x + 2y + 4z)²
(i) (x + 2y + 4z)² = x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca] = x² + 4y² + 16x² + 4xy + 16yz + 4zx
(i) (x + 2y + 4z)²
See less= x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca]
= x² + 4y² + 16x² + 4xy + 16yz + 4zx
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. y² + √2.
y² + √2 Polynomials in one variable as it contains only one variable y.
y² + √2 Polynomials in one variable as it contains only one variable y.
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