सोडोवचें [1/2x^2+1/4(1/2x-2)(x^2+4x-16)-(1/2x+2)+(x+3)^2]*[4x+9]

$$[ \frac { 1 } { 2 } x ^ { 2 } + \frac { 1 } { 4 } ( \frac { 1 } { 2 } x - 2 ) ( x ^ { 2 } + 4 x - 16 ) - ( \frac { 1 } { 2 } x + 2 ) + ( x + 3 ) ^ { 2 } ] \cdot [ 4 x + 9 ]$$

मूल्यांकन करचें

$$\frac{\left(4x+9\right)\left(x^{3}+12x^{2}+12x+120\right)}{8}$$

सोडोवणी पांवडे

\frac{1}{2}x-2 न \frac{1}{4} गुणपाक विभाजक विशमाचो वापर करचो.

$$\left(\frac{1}{2}x^{2}+\left(\frac{1}{8}x-\frac{1}{2}\right)\left(x^{2}+4x-16\right)-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

वितरक गूणधर्माचो वापर करून \frac{1}{8}x-\frac{1}{2} क x^{2}+4x-16 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

\frac{1}{2}x+2 चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\frac{1}{2}x-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

-\frac{9}{2}x मेळोवंक -4x आनी -\frac{1}{2}x एकठांय करचें.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+8-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

6 मेळोवंक 8 आनी 2 वजा करचे.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(a+b\right)^{2}=a^{2}+2ab+b^{2} विस्तारावचें \left(x+3\right)^{2}.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+x^{2}+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x^{2} मेळोवंक \frac{1}{2}x^{2} आनी x^{2} एकठांय करचें.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x मेळोवंक -\frac{9}{2}x आनी 6x एकठांय करचें.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+6+9\right)\left(4x+9\right)$$

15 मेळोवंक 6 आनी 9 ची बेरीज करची.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15\right)\left(4x+9\right)$$

वितरक गूणधर्माचो वापर करून \frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15 क 4x+9 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\frac{57}{8}x^{3}+\frac{39}{2}x^{2}+\frac{1}{2}x^{4}+\frac{147}{2}x+135$$

विस्तार करचो

$$\frac{x^{4}}{2}+\frac{57x^{3}}{8}+\frac{39x^{2}}{2}+\frac{147x}{2}+135$$

सोडोवणी पांवडे

\frac{1}{2}x-2 न \frac{1}{4} गुणपाक विभाजक विशमाचो वापर करचो.

$$\left(\frac{1}{2}x^{2}+\left(\frac{1}{8}x-\frac{1}{2}\right)\left(x^{2}+4x-16\right)-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

वितरक गूणधर्माचो वापर करून \frac{1}{8}x-\frac{1}{2} क x^{2}+4x-16 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\left(\frac{1}{2}x+2\right)+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

\frac{1}{2}x+2 चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-4x+8-\frac{1}{2}x-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

-\frac{9}{2}x मेळोवंक -4x आनी -\frac{1}{2}x एकठांय करचें.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+8-2+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

6 मेळोवंक 8 आनी 2 वजा करचे.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+\left(x+3\right)^{2}\right)\left(4x+9\right)$$

बायनोमियल प्रमेयाचो वापर करून \left(a+b\right)^{2}=a^{2}+2ab+b^{2} विस्तारावचें \left(x+3\right)^{2}.

$$\left(\frac{1}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+x^{2}+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x^{2} मेळोवंक \frac{1}{2}x^{2} आनी x^{2} एकठांय करचें.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}-\frac{9}{2}x+6+6x+9\right)\left(4x+9\right)$$

\frac{3}{2}x मेळोवंक -\frac{9}{2}x आनी 6x एकठांय करचें.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+6+9\right)\left(4x+9\right)$$

15 मेळोवंक 6 आनी 9 ची बेरीज करची.

$$\left(\frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15\right)\left(4x+9\right)$$

वितरक गूणधर्माचो वापर करून \frac{3}{2}x^{2}+\frac{1}{8}x^{3}+\frac{3}{2}x+15 क 4x+9 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\frac{57}{8}x^{3}+\frac{39}{2}x^{2}+\frac{1}{2}x^{4}+\frac{147}{2}x+135$$