Subtract (ap+bq-cr) from (a+b+c)(p+q+r) .

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Solution

(a + b + c)(p + q + r) - (ap + bq - cr)

= (ap + aq + ar + bp + bq + br + cp + cq + cr) - (ap + bq - cr)

Now,

= ap + aq + ar + bp + bq + br + cp + cq + cr - ap - bq + cr
= aq + ar + bp + br + cp + cq + 2cr

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