State True or False.
$a b (a^{2} + b^{2} - c^{2}) + b c (a^{2} + b^{2} - c^{2}) - c a (a^{2} + b^{2} - c^{2})$ $= (a^{2} + b^{2} - c^{2}) (a b + b c - c a)$

True

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False

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Solution

The correct option is A True
We have,
$a b (a^{2} + b^{2} - c^{2}) + b c (a^{2} + b^{2} - c^{2}) - c a (a^{2} + b^{2} - c^{2})$
$= (a^{2} + b^{2} - c^{2}) (a b + b c - c a)$

Suggest Corrections

Similar questions

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

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

\frac{a^{2} + b^{2} + a b}{b^{2} + c^{2} + b c} + \frac{c^{2} + c a + a^{2}}{b^{2} + c^{2} + b c}

Factorise by taking out the common factors:

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

a² + b² + c² - ab - bc - ca equals:

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} + b^{2} + c^{2} & b c + c a + a b & b c + c a + a b b c + c a + a b & a^{2} + b^{2} + c^{2} & b c + c a + a b b c + c a + a b & b c + c a + a b & a^{2} + b^{2} + c^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

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