Question

which of the following Expressions is in the simplest form

Answer 1

We are asked to find out which of the given expression is in the simplest form.

Let us analyze each of the given expression

Option 1:

$8m+4n-5mn+7$

It seems that this expression is already in its simplest form.

Option 2:

$15bd+5-2b+3d+23$

As you can see, the constant terms can be added together.

$\begin{gathered} 15bd-2b+3d+5+23 \\ 15bd-2b+3d+28 \end{gathered}$

So this expression was not in its simplest form.

Option 3:

$xy+6xy^2-7+12xy$

This expression may be further simplified as

$\begin{gathered} xy+6xy^2+12xy-7 \\ x(y+6y^2+12y)-7 \\ x(6y^2+13y)-7 \end{gathered}$

So this expression was not in its simplest form.

Option 4:

$35-a^2-ab^2+ab-2ab^2$

This expression may be further simplified as

$\begin{gathered} 35-a^2-ab^2+ab-2ab^2 \\ 35-a^2+ab-3ab^2 \end{gathered}$

So this expression was not in its simplest form.

Therefore, now we know for sure that expression 1 was in its simplest form.