Question

(a+b)(a-b+1)-(a-b)(a+b-1)

Answer 1

(a+b)(a-b+1)-(a-b)(a+b-1)=
=(а+b)(a-b)+(a+b)-
-(a-b)(a+b)+(a-b)=
=(a+b)+(a-b)= 2a

Answer 2

To simplify the given expression, let's expand it step-by-step:

Expression: (a+b)(a-b+1) - (a-b)(a+b-1)

Step 1: Expand the first part (a+b)(a-b+1) (a+b)(a-b+1) = a(a-b+1) + b(a-b+1)

Step 2: Distribute multiplication = a(a) + a(-b) + a(1) + b(a) - b(-b) + b(1) = a^2 - ab + a + ab - b^2 + b

Step 3: Simplify The 'ab' term cancels out, so we are left with: = a^2 - b^2 + a + b

Step 4: Expand the second part (a-b)(a+b-1) (a-b)(a+b-1) = a(a+b-1) - b(a+b-1)

Step 5: Distribute multiplication = a(a) + a(b) - a(1) - b(a) - b(b) + b(1) = a^2 + ab - a - ab - b^2 + b

Step 6: Simplify The 'ab' term cancels out, so we are left with: = a^2 - b^2 - a + b

Now, let's combine the two simplified parts:

(a+b)(a-b+1) - (a-b)(a+b-1) = (a^2 - b^2 + a + b) - (a^2 - b^2 - a + b)

Step 7: Remove the parentheses and combine like terms: = a^2 - b^2 + a + b - a^2 + b^2 + a - b

Step 8: Simplify further The 'a^2' and 'b^2' terms cancel out, and the 'a' and 'b' terms also cancel out, leaving us with:

= 0

So, the final simplified expression is 0.