Question

(a2+4)2-16a2=(a-2)2(a+2)2
докажите тождество​

Answer 1

a² - b² = (a - b)(a + b)

(a - b)² = a² - 2ab + b²

(a + b)² = a² + 2ab + b²

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(a² + 4)² - 16a² = (a² + 4)² - (4a)² = (a² + 4 - 4a)(a² + 4 + 4a) = (a² - 2*2*a + 2²)(a² + 2*2*a + 2²) = (a - 2)²(a+2)²  доказано