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Factorisation by Common Factors

Factorise by ...

Question

Factorise by taking out the common factors:

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

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Solution

ab(a²+ b²- c²) - bc(c²- a²- b²) + ca(a²+ b²- c²)

= ab(a²+ b²- c²) + bc(a²+ b²- c²) + ca(a²+ b²- c²)

= (a²+ b²- c²)[ab + bc + ca]

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Q. 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)

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

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

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

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

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Factorisation by Common Factors

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