Factorise: $(p^{2} - 2 p q + q^{2}) - r^{2}$

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Solution

We need to factorise $(p^{2} - 2 p q + q^{2}) - r^{2}$
We have $(p^{2} - 2 p q + q^{2}) - r^{2} = (p - q)^{2} - r^{2}$
By using $(a^{2} - b^{2}) = (a - b) (a + b)$
Here $a = (p - q), b = r$
Therefore, $(p^{2} - 2 p q + q^{2}) - r^{2} = (p - q - r) (p - q + r)$
Hence, factors are $(p - q - r) (p - q + r)$ .

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- r^{2} + p^{2} + q^{2} - 2 p q

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p^{2} - 2 p q + q^{2}

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Factorise: p^{2} + q^{2} + 2 (p q + q r + r p) .

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