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Question
Factorise the following by taking out the common factors:
p(p2 + q2 - r2) + q(r2 - q2 -p2) - r(p2 + q2 - r2)
Solution
p(p2 + q2 - r2) + q(r2 - q2 - p2) - r(p2 + q2 - r2)
= p(p2 + q2 - r2) - q(-r2 + q2 + p2) - r(p2 + q2 - r2)
= p(p2 + q2 - r2) - q(p2 + q2 - r2) - r(p2 + q2 - r2)
Here, the common factor is (p2 + q2 - r2).
Dividing throughout by (p2 + q2 - r2)
`("p"("p"^2 + "q"^2 - "r"^2))/("p"^2 + "q"^2 - "r"^2) - ("q"("p"^2 + "q"^2 - "r"^2))/(("p"^2 + "q"^2 - "r"^2)) - ("r"("p"^2 + "q"^2 - "r"^2))/(("p"^2 + "q"^2 - "r"^2))`
= p - q - r
∴ p(p2 + q2 - r2) + q(r2 - q2 - p2) - r(p2 + q2 - r2)
= (p2 + q2 - r2)(p - q - r).
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