Evaluate

21411

$21411$

Factor

3^{3}\times 13\times 61

$3_{3}×13×61$

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\begin{array}{c}\phantom{\times99}793\\\underline{\times\phantom{999}27}\\\end{array}

First line up the numbers vertically and match the places from the right like this.

\begin{array}{c}\phantom{\times99}793\\\underline{\times\phantom{999}27}\\\phantom{\times9}5551\\\end{array}

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 793 with 7. Write the result 5551 at the end leaving 0 spaces to the right like this.

\begin{array}{c}\phantom{\times99}793\\\underline{\times\phantom{999}27}\\\phantom{\times9}5551\\\underline{\phantom{\times}1586\phantom{9}}\\\end{array}

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 793 with 2. Write the result 1586 at the end leaving 1 spaces to the right like this.

\begin{array}{c}\phantom{\times99}793\\\underline{\times\phantom{999}27}\\\phantom{\times9}5551\\\underline{\phantom{\times}1586\phantom{9}}\\\phantom{\times}21411\end{array}

Now add the intermediate results to get final answer.

Examples

Quadratic equation

{ x } ^ { 2 } - 4 x - 5 = 0

$x_{2}−4x−5=0$

Trigonometry

4 \sin \theta \cos \theta = 2 \sin \theta

$4sinθcosθ=2sinθ$

Linear equation

y = 3x + 4

$y=3x+4$

Arithmetic

699 * 533

$699∗533$

Matrix

\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]

$[25 34 ][2−1 01 35 ]$

Simultaneous equation

\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.

${8x+2y=467x+3y=47 $

Differentiation

\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }

$dxd (x−5)(3x_{2}−2) $

Integration

\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x

$∫_{0}xe_{−x_{2}}dx$

Limits

\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}

$x→−3lim x_{2}+2x−3x_{2}−9 $