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secondary 3 | A Maths
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TitusLim
TitusLim

secondary 3 chevron_right A Maths chevron_right Singapore

Thx

Date Posted: 4 years ago
Views: 330
J
J
4 years ago
x³ + y³

= 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)
J
J
4 years ago
Or

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)
J
J
4 years ago
Alternatively,


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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Ho Jian Hian
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