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secondary 3 | A Maths
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Thx
= x(x²) + y(y²)
= x(x² + y² - y² + xy - xy ) + y(y² + x² - x² + xy - xy )
= x(x² - xy + y²) - xy² + x²y + y(x² - xy + y²) - x²y + xy²
= x(x² - xy + y²) + y(x² - xy + y²)
= (x + y)(x² - xy + y²)
x³ + y³
= x³ + y³ + xy² - xy² + x²y - x²y
= x³ - x²y + xy² + x²y - xy² + y³
= x(x² - xy + y²) + y(x² - xy + y²)
= (x + y)(x² - xy + y²)
let f(x) = x³ + y³
sub x = -y,
f(-y) = (-y)³ + y³ = 0
By the factor theorem, (x + y) is a factor of f(x)
x³ + y³ = (x + y)(x² - xy + y²)
(You can either figure this out by trialing or using long division)
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