2 + 82As we know, (x2 + Y2) = (x + y)2 – 2xy⇒ (x2)2 + 82⇒ (x2 + 8)2 – 2 × x2 × 8⇒ (x2 + 8)2 – (4x)2⇒ (x2 + 8 + 4x) (x2 + 8 – 4x)SHORT trick:⇒ x4 + 64Put x = 1, then⇒ 1 + 64⇒ 65From option 4⇒ (x2 + 4x + 8)(x2 – 4x + 8)⇒ 13 × 5⇒ 65 (satisfied)

"> 2 + 82As we know, (x2 + Y2) = (x + y)2 – 2xy⇒ (x2)2 + 82⇒ (x2 + 8)2 – 2 × x2 × 8⇒ (x2 + 8)2 – (4x)2⇒ (x2 + 8 + 4x) (x2 + 8 – 4x)SHORT trick:⇒ x4 + 64Put x = 1, then⇒ 1 + 64⇒ 65From option 4⇒ (x2 + 4x + 8)(x2 – 4x + 8)⇒ 13 × 5⇒ 65 (satisfied)

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A complete factorisation of x4 + 64 is:

General Aptitude Algebra in General Aptitude 1 year ago

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x4 + 64⇒ (x2)2 + 82As we know, (x2 + Y2) = (x + y)2 – 2xy⇒ (x2)2 + 82⇒ (x2 + 8)2 – 2 × x2 × 8⇒ (x2 + 8)2 – (4x)2⇒ (x2 + 8 + 4x) (x2 + 8 – 4x)SHORT trick:⇒ x4 + 64Put x = 1, then⇒ 1 + 64⇒ 65From option 4⇒ (x2 + 4x + 8)(x2 – 4x + 8)⇒ 13 × 5⇒ 65 (satisfied)

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