# 10 Deadly Common Algebra Mistakes

## Common Patterns of Algebra Mistakes

Students often make Common Algebra Mistakes due to confusion, such as expanding and simplifying 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 whether you make similar mistakes because, surprisingly, even university students still make these silly mistakes.

### Pattern 1

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

Many of students may think this is OK, but $\displaystyle \frac{4}{9} \ne \frac{2}{3}$. Do you think so?
$\displaystyle \sqrt{\frac{4}{9}} = \frac{2}{3}$ is TRUE!

### Pattern 2

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

Quite often, my students made this mistake in their school exams. Bad!
The correct solution would be;
\begin{aligned} \displaystyle x^2 &= 16 \\ x &= \pm 4 \end{aligned}

### Pattern 3

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

What do you think? You cannot cancel $x$ from both sides.
The correct solution would be;
\begin{aligned} \displaystyle x^2 &= 2x \\ x-2x &= 0 \\ x(x-2) &= 0 \\ x &= 0 \text{ or } x = 2 \end{aligned}

### Pattern 4

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

The correct solution would be;
$(x-3)^2 = x^2-6x + 9$

### Pattern 5

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

The correct solution would be;
$(x+3)^2 = x^2 +6x + 9$

### Pattern 6

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

The correct solution would be;
$\sqrt{(x+y)^2} = x + y$

### Pattern 7

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

The coefficient and the base cannot be multiplied.
The correct solution would be;
$3^x \times 2^x = 6^x$

### Pattern 8

$\sqrt{x^2} = x$

The outcome of the square root must be positive.
The correct solution would be;
$\sqrt{x^2} = |x|$

### Pattern 9

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

The correct solution would be;
\begin{aligned} \displaystyle a-\frac{b-c}{d} &= \frac{ad-(b-c)}{d} \\ &= \frac{ad-b+c}{d} \end{aligned}

### Pattern 10

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

You cannot cancel 2 at the numerator and 2 at the denominator.

Discover more enlightening videos by visiting our YouTube channel!

## Mastering Integration by Parts: The Ultimate Guide

Welcome to the ultimate guide on mastering integration by parts. If you’re a student of calculus, you’ve likely encountered integration problems that seem insurmountable. That’s…

## The Best Practices for Using Two-Way Tables in Probability

Welcome to a comprehensive guide on mastering probability through the lens of two-way tables. If you’ve ever found probability challenging, fear not. We’ll break it…

## Induction Made Simple: The Ultimate Guide

“Induction Made Simple: The Ultimate Guide” is your gateway to mastering the art of mathematical induction, demystifying a powerful tool in mathematics. This ultimate guide…

## High School Math for Life: Making Sense of Earnings

Salary Salary refers to the fixed amount of money that an employer pays an employee at regular intervals, typically on a monthly or biweekly basis,…