3 × 722 + 2 × 1022 – 44 when divided by 18 leaves the remainder______

<!- [if gte mso 9]><xml> </xml><! [endif]-> 3 × 7 2 2 + 2 × 1 0 2 2 − 4 4 = 3 × ( 1 + 6 ) 2 2 + 2 ( 1 + 9 ) 2 2 − 4 4 = 3 [ 1 + 2 2 C 1 × 6 + 2 2 C 2 × 6 2 + 2 2 C 3 × 6 3 + . . . . . 2 2 C 2 2 6 2 2 ] <!- [if gte mso 9]><xml> </xml><! [endif]-> = -39 on division by 18= (-54 + 15) on division by 18 = 15

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3 × 7²² + 2 × 10²² – 44 when divided by 18 leaves the remainder______

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alok kumar singh | Contributor-Level 10

2 months ago

$3 \times 7^{22} + 2 \times 1 0^{22} - 44 = 3 \times {(1 + 6)}^{22} + 2 {(1 + 9)}^{22} - 44$

$= 3 [1 +^{22} C_{1} \times 6 +^{22} C_{2} \times 6^{2} +^{22} C_{3} \times 6^{3} + . . . . .^{22} C_{22} 6^{22}]$

= -39 on division by 18

= (-54 + 15) on division by 18 = 15

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815988225"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mn>3</mn> <mo>×</mo> <msup> <mrow> <mn>7</mn> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mn>4</mn> <mo>=</mo> <mn>3</mn> <mo>×</mo> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>6</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>9</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mn>4</mn> </mrow> </math> <math> <mrow> <mo>=</mo> <mn>3</mn> <mrow> <mo> [</mo> <mrow> <mn>1</mn> <msup> <mrow> <mo>+</mo> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>×</mo> <mn>6</mn> <msup> <mrow> <mo>+</mo> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>×</mo> <msup> <mrow> <mn>6</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <msup> <mrow> <mo>+</mo> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo>×</mo> <msup> <mrow> <mn>6</mn> </mrow> <mrow> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msup> <mrow> <mo>.</mo> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msub> <msup> <mrow> <mn>6</mn> </mrow> <mrow> <mn>2</mn> <mn>2</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> </mrow> </math>              <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815988226"> </o:OLEObject></xml><! [endif]-> <div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754462254phpEzndzV.jpeg" alt="" width="403" height="36" loading="lazy"></picture></div></div>= -39 on division by 18= (-54 + 15) on division by 18 = 15

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