Maths puzzle someone please assist !

Supposing a = 1, b = 1

(1) a = b

(2) a×a = a×b

(3) a×a - b×b = a×b - b×b

(4) a×a + a×b - a×b - b×b = b×( a-b )

(5) a×( a+b ) - b×( a+b ) = b×( a-b )

(6) ( a+b )×( a-b ) = b×( a-b )

(7) a+b = b

(8) 2 = 1

Where is the mistake ?

You cannot go from step 6 to 7 because you are dividing both sides by zero...

a-b=0, so if you divide both sides by a-b, you are dividing both sides by zero, which is impossible.

The mistake is in step 6.
(6) ( a+b )×( a-b ) = b×( a-b )

If you expand the LHS ( a+b )×( a-b ), you get a^2 - b^2 (a squared minus b squared), which is different from your RHS.

Hello.

The mistake lies in going from line 6 to line 7. You cannot divide out the a-b in this problem. If a=b, then a-b=0, and so, you are dividing by 0. We know division by 0 is quite illegal.

Division by (a -- b) is not allowed as a = 1, b = 1 makes (a -- b) = 0.

The mistake is in step (6).Since a=b=1 then a-b=0.You can't divide by 0.
Step 7 is invalid