सोडोवचें 1/36(a-2b)^{3}[(a-2)^{2}(a+2)^{2}+4a^{2}-(2-a^2)^2]-ab(11/3b-a)-(1/3a-b)(b^2+a^2)

$$\frac { 1 } { 36 } ( a - 2 b ) ^ { 3 } [ ( a - 2 ) ^ { 2 } ( a + 2 ) ^ { 2 } + 4 a ^ { 2 } - ( 2 - a ^ { 2 } ) ^ { 2 } ] - a b ( \frac { 11 } { 3 } b - a ) - ( \frac { 1 } { 3 } a - b ) ( b ^ { 2 } + a ^ { 2 } )$$

मूल्यांकन करचें

$$-\frac{5b^{3}}{3}$$

सोडोवणी पांवडे

बायनोमियल प्रमेयाचो वापर करून \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} विस्तारावचें \left(a-2b\right)^{3}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(\left(a-2\right)^{2}\left(a+2\right)^{2}+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(p-q\right)^{2}=p^{2}-2pq+q^{2} विस्तारावचें \left(a-2\right)^{2}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(\left(a^{2}-4a+4\right)\left(a+2\right)^{2}+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(p+q\right)^{2}=p^{2}+2pq+q^{2} विस्तारावचें \left(a+2\right)^{2}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(\left(a^{2}-4a+4\right)\left(a^{2}+4a+4\right)+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

वितरक गूणधर्माचो वापर करून a^{2}-4a+4 क a^{2}+4a+4 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-8a^{2}+16+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

-4a^{2} मेळोवंक -8a^{2} आनी 4a^{2} एकठांय करचें.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(p-q\right)^{2}=p^{2}-2pq+q^{2} विस्तारावचें \left(2-a^{2}\right)^{2}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-\left(4-4a^{2}+\left(a^{2}\right)^{2}\right)\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

एक पॉवर दुसऱ्या पॉवरान उखलून धरपाक, निदर्शकांक गुणचें. 4 मेळोवंक 2 तल्यान 2 गुणचो.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-\left(4-4a^{2}+a^{4}\right)\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

4-4a^{2}+a^{4} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-4+4a^{2}-a^{4}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

12 मेळोवंक 16 आनी 4 वजा करचे.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+12+4a^{2}-a^{4}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

0 मेळोवंक -4a^{2} आनी 4a^{2} एकठांय करचें.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}+12-a^{4}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

0 मेळोवंक a^{4} आनी -a^{4} एकठांय करचें.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\times 12-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{1}{3} मेळोवंक \frac{1}{36} आनी 12 गुणचें.

$$\frac{1}{3}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

a^{3}-6a^{2}b+12ab^{2}-8b^{3} न \frac{1}{3} गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{3}a^{3}-2a^{2}b+4ab^{2}-\frac{8}{3}b^{3}-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{11}{3}b-a न ab गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{3}a^{3}-2a^{2}b+4ab^{2}-\frac{8}{3}b^{3}-\left(\frac{11}{3}ab^{2}-ba^{2}\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{11}{3}ab^{2}-ba^{2} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{1}{3}a^{3}-2a^{2}b+4ab^{2}-\frac{8}{3}b^{3}-\frac{11}{3}ab^{2}+ba^{2}-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{1}{3}ab^{2} मेळोवंक 4ab^{2} आनी -\frac{11}{3}ab^{2} एकठांय करचें.

$$\frac{1}{3}a^{3}-2a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}+ba^{2}-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

-a^{2}b मेळोवंक -2a^{2}b आनी ba^{2} एकठांय करचें.

$$\frac{1}{3}a^{3}-a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

b^{2}+a^{2} न \frac{1}{3}a-b गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{3}a^{3}-a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}-\left(\frac{1}{3}ab^{2}+\frac{1}{3}a^{3}-b^{3}-ba^{2}\right)$$

\frac{1}{3}ab^{2}+\frac{1}{3}a^{3}-b^{3}-ba^{2} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{1}{3}a^{3}-a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}-\frac{1}{3}ab^{2}-\frac{1}{3}a^{3}+b^{3}+ba^{2}$$

0 मेळोवंक \frac{1}{3}ab^{2} आनी -\frac{1}{3}ab^{2} एकठांय करचें.

$$\frac{1}{3}a^{3}-a^{2}b-\frac{8}{3}b^{3}-\frac{1}{3}a^{3}+b^{3}+ba^{2}$$

0 मेळोवंक \frac{1}{3}a^{3} आनी -\frac{1}{3}a^{3} एकठांय करचें.

$$-a^{2}b-\frac{8}{3}b^{3}+b^{3}+ba^{2}$$

-\frac{5}{3}b^{3} मेळोवंक -\frac{8}{3}b^{3} आनी b^{3} एकठांय करचें.

$$-a^{2}b-\frac{5}{3}b^{3}+ba^{2}$$

0 मेळोवंक -a^{2}b आनी ba^{2} एकठांय करचें.

$$-\frac{5}{3}b^{3}$$

विस्तार करचो

$$-\frac{5b^{3}}{3}$$

सोडोवणी पांवडे

बायनोमियल प्रमेयाचो वापर करून \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} विस्तारावचें \left(a-2b\right)^{3}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(\left(a-2\right)^{2}\left(a+2\right)^{2}+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(p-q\right)^{2}=p^{2}-2pq+q^{2} विस्तारावचें \left(a-2\right)^{2}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(\left(a^{2}-4a+4\right)\left(a+2\right)^{2}+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(p+q\right)^{2}=p^{2}+2pq+q^{2} विस्तारावचें \left(a+2\right)^{2}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(\left(a^{2}-4a+4\right)\left(a^{2}+4a+4\right)+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

वितरक गूणधर्माचो वापर करून a^{2}-4a+4 क a^{2}+4a+4 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-8a^{2}+16+4a^{2}-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

-4a^{2} मेळोवंक -8a^{2} आनी 4a^{2} एकठांय करचें.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-\left(2-a^{2}\right)^{2}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(p-q\right)^{2}=p^{2}-2pq+q^{2} विस्तारावचें \left(2-a^{2}\right)^{2}.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-\left(4-4a^{2}+\left(a^{2}\right)^{2}\right)\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

एक पॉवर दुसऱ्या पॉवरान उखलून धरपाक, निदर्शकांक गुणचें. 4 मेळोवंक 2 तल्यान 2 गुणचो.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-\left(4-4a^{2}+a^{4}\right)\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

4-4a^{2}+a^{4} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+16-4+4a^{2}-a^{4}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

12 मेळोवंक 16 आनी 4 वजा करचे.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}-4a^{2}+12+4a^{2}-a^{4}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

0 मेळोवंक -4a^{2} आनी 4a^{2} एकठांय करचें.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\left(a^{4}+12-a^{4}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

0 मेळोवंक a^{4} आनी -a^{4} एकठांय करचें.

$$\frac{1}{36}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)\times 12-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{1}{3} मेळोवंक \frac{1}{36} आनी 12 गुणचें.

$$\frac{1}{3}\left(a^{3}-6a^{2}b+12ab^{2}-8b^{3}\right)-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

a^{3}-6a^{2}b+12ab^{2}-8b^{3} न \frac{1}{3} गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{3}a^{3}-2a^{2}b+4ab^{2}-\frac{8}{3}b^{3}-ab\left(\frac{11}{3}b-a\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{11}{3}b-a न ab गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{3}a^{3}-2a^{2}b+4ab^{2}-\frac{8}{3}b^{3}-\left(\frac{11}{3}ab^{2}-ba^{2}\right)-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{11}{3}ab^{2}-ba^{2} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{1}{3}a^{3}-2a^{2}b+4ab^{2}-\frac{8}{3}b^{3}-\frac{11}{3}ab^{2}+ba^{2}-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

\frac{1}{3}ab^{2} मेळोवंक 4ab^{2} आनी -\frac{11}{3}ab^{2} एकठांय करचें.

$$\frac{1}{3}a^{3}-2a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}+ba^{2}-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

-a^{2}b मेळोवंक -2a^{2}b आनी ba^{2} एकठांय करचें.

$$\frac{1}{3}a^{3}-a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}-\left(\frac{1}{3}a-b\right)\left(b^{2}+a^{2}\right)$$

b^{2}+a^{2} न \frac{1}{3}a-b गुणपाक विभाजक विशमाचो वापर करचो.

$$\frac{1}{3}a^{3}-a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}-\left(\frac{1}{3}ab^{2}+\frac{1}{3}a^{3}-b^{3}-ba^{2}\right)$$

\frac{1}{3}ab^{2}+\frac{1}{3}a^{3}-b^{3}-ba^{2} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{1}{3}a^{3}-a^{2}b+\frac{1}{3}ab^{2}-\frac{8}{3}b^{3}-\frac{1}{3}ab^{2}-\frac{1}{3}a^{3}+b^{3}+ba^{2}$$

0 मेळोवंक \frac{1}{3}ab^{2} आनी -\frac{1}{3}ab^{2} एकठांय करचें.

$$\frac{1}{3}a^{3}-a^{2}b-\frac{8}{3}b^{3}-\frac{1}{3}a^{3}+b^{3}+ba^{2}$$

0 मेळोवंक \frac{1}{3}a^{3} आनी -\frac{1}{3}a^{3} एकठांय करचें.

$$-a^{2}b-\frac{8}{3}b^{3}+b^{3}+ba^{2}$$

-\frac{5}{3}b^{3} मेळोवंक -\frac{8}{3}b^{3} आनी b^{3} एकठांय करचें.

$$-a^{2}b-\frac{5}{3}b^{3}+ba^{2}$$

0 मेळोवंक -a^{2}b आनी ba^{2} एकठांय करचें.

$$-\frac{5}{3}b^{3}$$