Question

Simplify
(i) (a² - 6²)²
(ii) (2x + 5)² - (2x - 5)²
(iii) (7m - 8n)² + (7m + 8n)²
(iv) (4m + 5n)² + (5m + 4n)²
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Answer 1

Answer:

(i) a⁴ - 72a² + 1296

(ii) 40x

(iii) 98m² + 128n²

(iv) 41m² + 80mn + 41n²

Step-by-step explanation:

(i) (a² - 6²)²

=> (a² - 36)²

=> Use (a - b)² = a² - 2ab + b²

=> a⁴ - 72a² + 1296

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(ii) (2x + 5)² - (2x - 5)²

=> Using a² - b² = (a - b)(a + b)

=> 10 × 40x

=> 400x

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(iii) (7m - 8n)² + (7m + 8n)²

=> Using (a - b)² = a² - 2ab + b²

=> 49m² - 112mn + 64n² + (7m + 8n)²

=> 49m² - 112mn + 64n² + 49m² + 112mn + 64n²

=> 49m² + 64n² + 49m² + 64n²

=> 98m² + 128n²

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(iv) (4m + 5n)² + (5m + 4n)²

=> Using (a + b)² = a² + 2ab + b²

=> 16m² + 40mn + 25n² + (5m + 4n)²

=> 16m² + 40mn + 25n² + 25m² + 40mn + 16n²

=> 41m² + 40mn + 25n² + 40mn + 16n²

=> 41m² + 80mn + 41n²

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