Factorise: $a^{2} b + a b^{2} - a b c - b^{2} c + a x y + b x y$

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Solution

$(a^{2} b - a b c + a x y) + (a b^{2} - b^{2} c + b x y)$
$a (a b - b c + x y) + b (a b - b c + x y)$
$(a + b) (a b - b c + x y)$

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\frac{a^{3}}{8} + \frac{b^{3}}{27} + \frac{a^{2} b}{4} + \frac{a b^{2}}{6}

A = a^{2} b + a b^{2} - a^{2} c - a c^{2},

B = b^{2} c + b c^{2} - a^{2} b - a b^{2}

C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

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A x^{2} + B x + C = 0

a, b, c

A, B, C

A = a^{2} b + a b^{2} - a^{2} c - a c^{2}, B = b^{2} c + b c^{2} - a^{2} b - a b^{2}, C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

a > b > c > 0

A x^{2} + B x + C = 0

a, b, c

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