Question

Q.1. Use the digits 2 and 8 to make two distinct 2-digit numbers. These numbers are 28 and 82. Now, find the difference of squares of these numbers. 822– 282= 6724 – 784 = 5940 = 11 × 540 = 99 × 60 = 99 × 10 × 6 = 99 ×(8 + 2) (8 – 2) = 99 × sum of the digits × difference of the digits. Taking the digits as x and y prove that (xy)2-(yx)2=99 (x+y)(x-y) [Note: Here, xyis a 2-digit number, not the product of x and y.] Try the above with other pairs of digits and verify that it always works.

Answer 1

$$\begin{gathered} \mathrm{Take}\mathrm{x}=5\mathrm{and}\mathrm{y}=2. \\ \mathrm{LHS} \\ {\left(52\right)}^2-{\left(25\right)}^2=2704-625=2079 \\ \mathrm{RHS} \\ 99\left(5+2\right)\left(5-2\right)=99\left(7\right)\left(3\right)=2079 \\ \mathrm{LHS}=\mathrm{RHS} \\ \mathrm{Hence}\mathrm{Proved}. \end{gathered}$$