Q. 2 B4.0( 2 Votes )

# In the multiplication table made earlier, take a square of nine numbers, instead of four, and mark the numbers at the four corners:

Explain using algebra, why this difference is the same for all such squares.

Answer :

we can write a row of multiplication table as

x 2x 3x 4x 5x 6x 7x 8x 9x

Next row will be:

(x+1) 2(x+1) 3(x+1) 4(x+1) 5(x+1) 6(x+1) 7(x+1) 8(x+1) 9(x+1)

If we take a general number from the first row as yx then the next number in this row will be (y+1)x.

So, we can obtain a general square of 9 terms from this multiplication table as:

Diagonal sums: (yx)+(y+2)(x+2) = yx+y(x+2)+2(x+2) = yx + yx + 2y +2x +4

= 2yx +2y +2x +4

Y(x+2)+ (y+2)x = (yx +2y)+(yx + 2x) = 2yx +2y +2x

Clearly, the difference between diagonal sums is equal to 4.

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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