Q. 1 C5.0( 4 Votes )
Write number like this:

Instead of a square of four numbers, take a square of nine numbers and mark only the numbers at the four corners.

What is the difference of diagonal products? Explain using algebra.
Answer :
Consider the green square and consider the four corner elements ( red circles)
Diagonal products: 1× 13 = 13
3× 11 = 33
Difference between diagonal products = 33 - 13 = 20
Now, consider this green square and consider the corner elements (red circles)
Diagonal products: 8× 20 = 160
18× 10 = 180
Difference between diagonal products = 180 – 160 = 20
So, we observe that the difference between diagonal products in the above cases is also coming out to be same and is equal to 20.
Explanation using Algebra,
Let the first number in the square be x, the others can be filled in as below,
Diagonal products: x (x+12) = x2 + 12x
(x+10)(x+2) = x(x+2) + 10(x+2) = (x2 + 2x) + (10x+ 20)
= x2 + 12x + 20
Clearly, we can observe that the difference between diagonal products is always equal to 20.
Rate this question :






















Write number like this:
As in the calendar; mark four numbers in a square and find the difference of diagonal products. Is it the same for all squares of four numbers?
Kerala Board Mathematics Part IIn the multiplication table made earlier, take a square of nine numbers, instead of four, and mark the numbers at the four corners:
What if we take a square of sixteen numbers?
Kerala Board Mathematics Part IWrite number like this:
Instead of a square of four numbers, take a square of nine numbers and mark only the numbers at the four corners.
What is the difference of diagonal products? Explain using algebra.
Kerala Board Mathematics Part IWrite number like this:
As in the calendar; mark four numbers in a square and find the difference of diagonal products. Is it the same for all squares of four numbers?
Kerala Board Mathematics Part IWrite number like this:
Instead of a square of four numbers, take a square of nine numbers and mark only the numbers at the four corners.
What is the difference of diagonal products? Explain using algebra.
Kerala Board Mathematics Part IWrite number like this:
Explain why this is so, using algebra.
Kerala Board Mathematics Part IIn the multiplication table made earlier, take a square of nine numbers, instead of four, and mark the numbers at the four corners:
What if we take a square of sixteen numbers?
Kerala Board Mathematics Part IIn the multiplication table made earlier, take a square of nine numbers, instead of four, and mark the numbers at the four corners:
What is the difference of diagonal sums?
Kerala Board Mathematics Part IWrite number like this:
Explain why this is so, using algebra.
Kerala Board Mathematics Part I