90x²-y²-10 factorize
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(i) x²+y²
≡ (x+y)²-2xy
≡ (x+y+√(2xy))(x+y-√(2xy))
(ii) x²+y²
≡ x²-(iy)²
≡ (x+iy)(x-iy)
(iii) x²+y²
≡y²+x²
≡y²-(ix)²
≡(y+ix)(y-ix)
(iv) x²+y²
≡ (x-y)²+2xy
≡(x-y)²-(i√2xy)²
≡ {x-y+i√(2xy)}{x-y-i√(2xy)}
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How do I factorise x²+y²?
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Factorising into (i) real, (ii) complex factors .
(i) x²+y²
≡ (x+y)²-2xy
≡ (x+y+√(2xy))(x+y-√(2xy))
(ii) x²+y²
≡ x²-(iy)²
≡ (x+iy)(x-iy)
(iii) x²+y²
≡y²+x²
≡y²-(ix)²
≡(y+ix)(y-ix)
(iv) x²+y²
≡ (x-y)²+2xy
≡(x-y)²-(i√2xy)²
≡ {x-y+i√(2xy)}{x-y-i√(2xy)}
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