What is the LCM of $a^{3} b - a b^{3}, a^{3} b^{2} + a^{2} b^{3}$ and $a b (a + b)$ ?

a^{2} b^{2} (a^{2} - b^{2})

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a b (a^{2} - b^{2})

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a^{2} b^{2} + a b^{3}

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a^{3} b^{3} (a^{2} - b^{2})

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Solution

The correct option is A $a^{2} b^{2} (a^{2} - b^{2})$
$x = a^{3} b - a b^{3} = a b (a^{2} - b^{2}) = a b (a - b) (a + b)$
$y = a^{3} b^{2} + a^{2} b^{3} = a^{2} b^{2} (a + b)$
$z = a b (a + b)$
$L C M = a^{2} b^{2} (a + b) (a - b)$
$= a^{2} b^{2} (a^{2} - b^{2})$

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Similar questions

A = [\begin{matrix} a b & b^{2} {- a}^{2} & - a b \end{matrix}]

2

A^{2} = A . A = [\begin{matrix} a^{2} b^{2} - & a^{2} b^{2} {- a}^{3} b + & a^{3} b \end{matrix} \begin{matrix} a b^{3} - & {a b}^{3} {- a}^{2} b^{2} + & a^{2} b^{2} \end{matrix}]

[\begin{matrix} 0 & 0 0 & 0 \end{matrix}] = O

A

2

(a^{2} + b^{2} + c^{2})^{3} + 2 (b c + c a + a b)^{3} - 3 (a^{2} + b^{2} + c^{2}) (b c + c a + a b)^{2} = (a^{3} + b^{3} + c^{3} - 3 a b c)^{2}

\frac{2 b + a - \frac{4 a^{2} - b^{2}}{a}}{b^{3} + 2 a b^{2} - 3 a^{2} b} \cdot \frac{a^{3} b - 2 a^{2} b^{2} + a b^{3}}{a^{2} - b^{2}}

The length of the chord intercepted by the circle $x^{2} + y^{2} = r^{2}$ on the line $\frac{x}{a} + \frac{y}{b} = 1$

a b (a^{2} + b^{2} - c^{2}) + b c (a^{2} + b^{2} - c^{2}) - c a (a^{2} + b^{2} - c^{2})

= (a^{2} + b^{2} - c^{2}) (a b + b c - c a)

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