1=2?1 =2?

Algebra Level 2

Let's prove that 1=21 =2 by using two variables, aa and bb. Before we start, let's let a=ba=b. Now, we can prove that 1=21=2. 1) a=b  Given1) \ a = b \ || \ \text{Given}

2) a2=ab  Multiply both sides by a2) \ a^2=ab \ || \ \text{Multiply both sides by} \ a

3) a2b2=abb2  Subtract both sides by b23) \ a^2-b^2=ab-b^2 \ || \ \text{Subtract both sides by} \ b^2

4) (a+b)(ab)=b(ab)  Factor both sides4) \ (a+b)(a-b)=b(a-b) \ || \ \text{Factor both sides}

5) (a+b)=b  Divide both sides by (ab)5) \ (a+b)=b \ || \ \text{Divide both sides by} \ (a-b)

6) a+a=a  Substitute a for b6) \ a + a = a \ || \ \text{Substitute} \ a \ \text{for} \ b

7) 2a=a  Addition7) \ 2a = a \ || \ \text{Addition}

8) 2=1  Divide both sides by a8) \ 2 = 1 \ || \ \text{Divide both sides by} \ a

Which step is incorrect?

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