Simplify each of the following:
(i) 175 × 175 + 2 × 175 × 25 + 25 ×25
(ii) 322 × 322 – 2 × 322 × 22 + 22 × 22
(iii) 0.76 ×0.76+2×0.76×0.24+0.24×0.24
(iv)7.83 x 7.83 - 1.17 x 1.17 /6.66
Answers
(i) Given : 175 x 175 + 2 x 175 x 25 + 25 x 25
= (175)² + 2 (175) (25) + (25)²
= (175 + 25)²
Let a = 175 & b = 25
[We know that a² + b² + 2ab = (a + b)² ]
= (200)²
= 40000
Hence, 175 x 175 + 2 x 175 x 25 + 25 x 25 = 40000
(ii) Given : 322 x 322 – 2 x 322 x 22 + 22 x 22
= (322)² – 2 x 322 x 22 + (22)²
= (322 – 22)²
Let a = 322 & b = 22
[We know that a² + b² - 2ab = (a - b)² ]
= (300)²
= 90000
Hence, 322 x 322 – 2 x 322 x 22 + 22 x 22 = 90000.
(iii) Given : 0.76 x 0.76 + 2 x 0.76 x 0.24 + 0.24 x 0.24
= (0.76)² + 2 x 0.76 x 0.24 + (0.24)²
= (0.76 + 0.24)²
Let a = 0.76 & b = 0.24
[We know that a² + b² + 2ab = (a + b)² ]
= (1.00)²
= 1
Hence, 0.76 x 0.76 + 2 x 0.76 x 0.24 + 0.24 x 0.24 = 1
(iv) Given : 7.83 x 7.83 - 1.17 x 1.17 /6.66
= (7.83² - 1.17²)/6.66
[We know that a² - b² = (a + b) (a -b)]
= [ (7.83 + 1.17) (7.83 + 1.17)]/6.66
= [9 × 6.66]/ 6.66
= 9
Hence,7.83 x 7.83 - 1.17 x 1.17 /6.66 = 9
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Answer:
Step-by-step explanation:
(i) Given : 175 x 175 + 2 x 175 x 25 + 25 x 25
= (175)² + 2 (175) (25) + (25)²
= (175 + 25)²
Let a = 175 & b = 25
[We know that a² + b² + 2ab = (a + b)² ]
= (200)²
= 40000
Hence, 175 x 175 + 2 x 175 x 25 + 25 x 25 = 40000
(ii) Given : 322 x 322 – 2 x 322 x 22 + 22 x 22
= (322)² – 2 x 322 x 22 + (22)²
= (322 – 22)²
Let a = 322 & b = 22
[We know that a² + b² - 2ab = (a - b)² ]
= (300)²
= 90000
Hence, 322 x 322 – 2 x 322 x 22 + 22 x 22 = 90000.
(iii) Given : 0.76 x 0.76 + 2 x 0.76 x 0.24 + 0.24 x 0.24
= (0.76)² + 2 x 0.76 x 0.24 + (0.24)²
= (0.76 + 0.24)²
Let a = 0.76 & b = 0.24
[We know that a² + b² + 2ab = (a + b)² ]
= (1.00)²
= 1
Hence, 0.76 x 0.76 + 2 x 0.76 x 0.24 + 0.24 x 0.24 = 1
(iv) Given : 7.83 x 7.83 - 1.17 x 1.17 /6.66
= (7.83² - 1.17²)/6.66
[We know that a² - b² = (a + b) (a -b)]
= [ (7.83 + 1.17) (7.83 + 1.17)]/6.66
= [9 × 6.66]/ 6.66
= 9