A এর উৎপাদকগুলো নির্ণয় কর।

Question

Accepted Answer

দেওয়া আছে, $A=P^4(q-r)+q^4(r-p)+r^4(p-q)$ $\begin{aligned} & =p^4(q-r)+q^4 r-p q^4+p r^4-q r^4 \ & =p^4(q-r)+q r\left(q^3-r^3ight)-p\left(q^4-r^4ight) \ & =(q-r)\left\{p^4+q r\left(q^2+q r+r^2ight)-p(q+r)\left(q^2+r^2ight)ight\} \ & =(q-r)\left\{p^4+q r\left(q^2+q r+r^2ight)-p\left(q^3+q r^2+q^2 r+r^3ight)ight\} \ & =(q-r)\left\{p^4+q^3 r+q^2 r^2+q r^3-p q^3-p q r^2-p q^2 r-p r^3ight\} \ & =(q-r)\left\{p\left(p^3-q^3ight)-r^3(p-q)-q^2 r(p-q)-q r^2(p-q)ight\} \ & =(q-r)(p-q)\left\{p\left(p^2+p q+q^2ight)-r^3-q^2 r-q r^2ight\} \ & =(q-r)(p-q)\left(p^3+p^2 q+p q^2-r^3-q^2 r-q r^2ight) \ & =(q-r)(p-q)\left\{-q^2(r-p)-q\left(r^2-p^2ight)-\left(r^3-p^3ight)ight\} \ & =(q-r)(p-q)(r-p)\left\{-q^2-q(r+p)-\left(r^2+r p+p^2ight)ight\} \ & =(q-r)\left(p^{\prime}-qight)(r-p)\left\{-q^2-q r-p q-r^2-p-p^2ight\} \ & =-(p-q)(q-r)(r-p)\left(p^2+q^2+r^2+p q+q r+pight)\end{aligned}$ নির্ণেয় উৎপাদক $-(p-q)(q-r)(r-p)\left(p^2+q^2+r^2+p q+q r+r pight)$.

SSC উচ্চতর গণিত CQ — A এর উৎপাদকগুলো নির্ণয় কর।

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