# Common Patterns of Algebra Mistakes

Students often make Common Algebra Mistakes due to confusions such as expand and simplify rules, fractions, indices and equations which that lead the students to the wrong answer. Also these error patterns are very basic and quite easily rectified. Check yourself whether you make similar mistakes, because surprisingly even students in the university are still making these silly mistakes.
Let me start with very simple patterns.

### Pattern 1

$$\displaystyle \frac{4}{9} = \frac{2}{3}$$

### Pattern 2

\begin{aligned} \displaystyle x^2 &= 16 \\ x &= 4 \\ \end{aligned}

### Pattern 3

\begin{aligned} \displaystyle x^2 &= 2x \\ x &= 2 \\ \end{aligned}

### Pattern 4

$$(x-3)^2 = x^2 -9$$

### Pattern 5

$$(x+3)^2 = x^2 +9$$

### Pattern 6

$$\sqrt{x^2 + y^2} = x + y$$

### Pattern 7

$$3 \times 2^x = 6^x$$

### Pattern 8

$$\sqrt{x^2} = x$$

### Pattern 9

$$\displaystyle a-\frac{b-c}{d} = \frac{ad-b-c}{d}$$

### Pattern 10

\begin{aligned} \displaystyle \frac{x-2}{2} &= \frac{x – 1}{1} \\ &= x-1 \end{aligned}