Solve using formula Ekanyunena poorvena: 48 × 9

Given, 48 × 9 Ekanyunena Poorvena Vidhi (method) (meaning one less than before): This formula is used when one of the numbers is made up of 9 s . Steps: Reduce multiplicand by one and keep multiplier as it is following this. Then subtract (multiplicand minus one) from the result of previous step. To multiply 48 × 9 using Ekanyunena poorvena method: Reduce 48 by 1 and keep 9 as it is following this. we get 479 Then subtract 47 from this number 479 to get the solution. 479 - 47 432 Hence, 48 × 9 = 432

Solve the given expression x + 4 × x + 4 using Urdhwatriyak vidhi and check the answer.

We need to multiply the expression x + 4 × x + 4 ,by using Urdhwatriyak vidhi, x + 4 × x + 4 So,we follow the steps as, 1 . + 4 + 4 16 (first column,vertical multiplication) 2 . x + 4 × x + 4 4 x + 4 x = 8 x (first column × second column,diagonal multiplication) 3 . x × x x 2 (third column,vertical multiplication) Therefore, x + 4 × x + 4 = x 2 + 8 x + 16 To check the answer,we do, Digit sum of numerical coefficient of first expression × Digit sum of numerical coefficient of second expression = Digit sum of numerical coefficient of the answer. Here,Digit sum of numerical coefficient of first expression = 5 Digit sum of numerical coefficient of second expression = 5 Digit sum of numerical coefficient of answer = 1 + 8 + 16 = 25 Hence by using the given formula to check we get that, 5 × 5 = 25

Divide by Paravartya Yojayet method, 1432 ÷ 88 .

Steps for division: (i) Take the nearest base of 88 , i.e. 100 (ii) Difference: 100 - 88 = 12 (iii) Write 12 in the second row and add the digits in the middle column. (iv) Write the product of 5 and 12 (consider individual digits), i.e. 5 and 10 in the third column and third row. (v) Add the digits to get the result such as 15 and 112 . (vi) 112 > 88 , so place 1 below 5 and - 88 in the last column. (vii) Add the digits in the middle column and subtract the third column. Therefore, quotient = 16 and remainder = 24

Solve the given expression 4 x + 2 y × 3 x + 3 y using Urdhwatriyak vidhi and check the answer.

We need to multiply the expression 4 x + 2 y × 3 x + 3 y ,by using Urdhwatriyak vidhi, 4 x + 2 y × 3 x + 3 y So,we follow the steps as, 1 . + 2 y + 3 y 6 y 2 (first column,vertical multiplication) 2 . 4 x + 2 y × 3 x + 3 y 12 xy + 6 xy = 18 xy (first column × second column,diagonal multiplication) 3 . 4 x × 3 x 12 x 2 (third column,vertical multiplication) Therefore, 4 x + 2 y × 3 x + 3 y = 12 x 2 + 18 xy + 6 y 2 To check the answer,we do, Digit sum of numerical coefficient of first expression × Digit sum of numerical coefficient of second expression = Digit sum of numerical coefficient of the answer. Here,Digit sum of numerical coefficient of first expression = 6 Digit sum of numerical coefficient of second expression = 6 Digit sum of numerical coefficient of answer = 12 + 18 + 6 = 36 Hence by using the given formula to check we get that, 6 × 6 = 36

Solve the given expression x 2 + 2 x + 1 × x 2 + 3 x + 4 using Urdhwatriyak vidhi and check the answer.

We need to multiply the expression x 2 + 2 x + 1 × x 2 + 3 x + 4 ,by using Urdhwatriyak vidhi, x 2 + 2 x + 1 × x 2 + 3 x + 4 So,we follow the steps as, 1 . + 1 + 4 4 (first column,vertical multiplication) 2 . 2 x + 1 × 3 x + 4 8 x + 3 x = 11 x (first column × second column,diagonal multiplication) 3 . x 2 + 2 x + 1 × x 2 + 3 x + 4 4 x 2 + x 2 + 6 x 2 = 11 x 2 (as per signs multiply first and third term diagonally and second by second vertically and add) 4 . x 2 + 2 x × x 2 + 3 x 3 x 3 + 2 x 3 = 5 x 3 (second and third column,diagonal multiplication) 5 . x 2 × x 2 x 4 (third column vertical multiplication) Therefore, x 2 + 2 x + 1 × x 2 + 3 x + 4 = x 4 + 5 x 3 + 11 x 2 + 11 x + 4 To check the answer,we do, Digit sum of numerical coefficient of first expression × Digit sum of numerical coefficient of second expression = Digit sum of numerical coefficient of the answer. Here,Digit sum of numerical coefficient of first expression = 4 Digit sum of numerical coefficient of second expression = 8 Digit sum of numerical coefficient of answer = 1 + 5 + 11 + 11 + 4 = 32 Hence by using the given formula to check we get that, 4 × 8 = 32

Solve the given expression x - 3 y × x + 3 y using Urdhwatriyak vidhi and check the answer.

We need to multiply the expression x - 3 y × x + 3 y ,by using Urdhwatriyak vidhi, x - 3 y × x + 3 y So,we follow the steps as, 1 . - 3 y + 3 y - 9 y 2 (first column,vertical multiplication) 2 . x - 3 y × x + 3 y 3 x y - 3 xy = 0 (first column × second column,diagonal multiplication) 3 . x × x x 2 (third column,vertical multiplication) Therefore, x - 3 y × x + 3 y = x 2 - 9 y 2 To check the answer,we do, Digit sum of numerical coefficient of first expression × Digit sum of numerical coefficient of second expression = Digit sum of numerical coefficient of the answer. Here,Digit sum of numerical coefficient of first expression = - 2 Digit sum of numerical coefficient of second expression = 4 Digit sum of numerical coefficient of answer = - 8 Hence by using the given formula to check we get that, - 2 × 4 = 8

Divide by Paravartya Yojayet method, 1154 ÷ 103 .

Steps for division: i Take the nearest base of 103 , i.e. 100 i i Difference: 103 - 100 = 03 i i i Take the bar for 3 and write as shown below. i v Write 03 in the second row and product of 1 and 03 in the third column and third row. v Subtract the digits to get the final result. Hence, the quotient = 11 and the remainder = 21 .