Solve the given expression 4 x + 1 × x + 5 using Urdhwatriyak vidhi and check the answer.

We need to multiply the expression 4 x + 1 × x + 5 ,by using Urdhwatriyak vidhi, 4 x + 1 × x + 5 So,we follow the steps as, 1 . + 1 + 5 + 5 (first column,vertical multiplication) 2 . 4 x + 1 × x + 5 4 x × 5 + x = 21 x (first column × second column,diagonal multiplication) 3 . 4 x × x 4 x 2 (third column,vertical multiplication) Therefore, 4 x + 1 × x + 5 = 4 x 2 + 21 x + 5 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 x + 1 = 5 Digit sum of numerical coefficient of second expression x + 5 = 6 Digit sum of numerical coefficient of answer = 30 Hence by using the given formula to check we get that, 5 × 6 = 30

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 - 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

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

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 2 x 2 + 3 y - 4 × 3 x 2 + 4 y + 5 using Urdhwatriyak vidhi and check the answer.

We need to multiply the expression 2 x 2 + 3 y - 4 × 3 x 2 + 4 y + 5 ,by using Urdhwatriyak vidhi, 2 x 2 + 3 y - 4 × 3 x 2 + 4 y + 5 So,we follow the steps as, 1 . - 4 + 5 - 20 (first column,vertical multiplication) 2 . 3 y - 4 × 4 y + 5 15 y - 16 y = - y (first column × second column,diagonal multiplication) 3 . 2 x 2 + 3 y - 4 × 3 x 2 + 4 y + 5 10 x 2 + - 12 x 2 + 12 y 2 = - 2 x 2 + 12 y 2 (as per signs multiply first and third term diagonally and second by second vertically and add) 4 . 2 x 2 + 3 y × 3 x 2 + 4 y 8 x 2 y + 9 x 2 y = 17 x 2 y (second and third column,diagonal multiplication) 5 . 2 x 2 × 3 x 2 6 x 4 (third column vertical multiplication) Therefore, 2 x 2 + 3 y - 4 × 3 x 2 + 4 y + 5 = 6 x 4 + 17 x 2 y - 2 x 2 + 12 y 2 - y - 20 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 = 1 Digit sum of numerical coefficient of second expression = 12 Digit sum of numerical coefficient of answer = 6 + 17 - 2 + 12 - 1 - 20 = 12 Hence by using the given formula to check we get that, 12 × 1 = 12