Q. 3 B4.0( 3 Votes )

# Take nine numbers forming a square in a calendar and mark the four numbers at the corners.Multiply the diagonal pairs and find the difference of these products.3 × 19 = 5717 × 5 = 8585 – 57 = 28Explain using algebra, why the difference is always 28 (It is convenient to take the number at the centre as x).

Let’s use algebra to see this.

Taking the first number in the square as x, the others can be filled as below

Multiply the diagonal pairs

(x)(x+16)

= x2+16x

Other diagonal product

(x+14)(x+2) [using identity (x+y)(u+v)= xu+xv+yu+yv]

= x2+2x+14x+28

= x2+16x+28

Difference of these products

=(x2+16x+28) - (x2+16x)

=x2+16x+28 - x2-16x

= 28

Hence the difference is 28, we can take any number as x; which means this hold in any part of the calendar.

We can take x at the center, but this will complicate our calculations.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Algebric Identities46 mins
Discussion on Algebric Identities48 mins
Algebric Expressions and Identities45 mins
Algebraic Expressions and Identities43 mins
Master Algebraic Identities43 mins
Division of Algebraic Expressions36 mins
Smart Revision | Quiz on Algebraic Expression and Identities44 mins
How to Use Algebraic Identities40 mins
Multiplication of Algebraic Expression40 mins
Genius Quiz | Algebraic Expressions and Identities30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses