### Theory:

Let us look at the division of algebraic expression:

$\frac{3x+2}{2}=\frac{3x+\overline{)2}}{\overline{)2}}=3x$

Can you think the above expression solved correctly?

Of course, No!

This is because when the numerator is connected by the terms we cannot directly cancel the values from numerator and denominator.

Therefore, the procedure applied to solve the above algebraic expression is wrong.
Example:
Let us look for some general error that we have done while solving the exercises involves algebraic expressions.

1. $$3(x+2) = 3x+2$$ - In this case, we need to apply distributive law to find the result. The number $$3$$ should be multiplied over both the values inside the bracket. That is $$3x+6$$.

2. $$6x+2y = 8xy$$ - In this case, we cannot add the terms with different variable.

3.  $\frac{4{x}^{3}+6}{4{x}^{3}}=1+6=7$ - In this case, we cannot cancel the term $$4x^3$$.
4. Substitute $$z = -2$$ in the expression $$z^2 + 8z$$ gives $$(– 2)^2+ 8(–2) = – 4 – 16 = – 20$$ - In this case, square of negative number$$(-2)^2 = 4$$ becomes positive number.
5. $\frac{4{y}^{5}}{4{y}^{5}}=0$ - In this case, the term $$4y^5$$ gets cancelled and results in $$1$$.