To set up the expression, evaluate part by part.  Let \(\displaystyle x\) be the unknown number.

Eight times a number:  \(\displaystyle 8x\)

Twenty less than eight times the number means that this product is subtracted twenty.  The final answer must be less than eight times the unknown number by twenty.

The correct answer is:  \(\displaystyle 8x-20\)

Separate the statement by parts.

The difference of \(\displaystyle x\) and \(\displaystyle 5\):  \(\displaystyle x-5\)

Square of a the difference of \(\displaystyle x\) and \(\displaystyle 5\):  \(\displaystyle (x-5)^2\)

The correct answer is:  \(\displaystyle (x-5)^2\)

Split up the sentence into parts.

A number squared:  \(\displaystyle x^2\)

Three times a number squared:  \(\displaystyle 3x^2\)

Six less than three times a number squared:  \(\displaystyle 3x^2-6\)

The squared quantity of six less than three times a number squared:  \(\displaystyle (3x^2-6)^2\)

The answer is:  \(\displaystyle (3x^2-6)^2\)

Break up the sentence into parts.

A number cubed:  \(\displaystyle x^3\)

The square root of a number cubed:  \(\displaystyle \sqrt{x^3}\)

Seven more than the square root of a number cubed: \(\displaystyle \sqrt{x^3}+7\)

The answer is:  \(\displaystyle \sqrt{x^3}+7\)

Write the expression by splitting up the statement into parts.

Six times a number:  \(\displaystyle 6x\)

The square root of six times a number:  \(\displaystyle \sqrt{6x}\)

The expression is:  \(\displaystyle \sqrt{6x}\)

Let \(\displaystyle x\) be a number, and let \(\displaystyle y\) be another number.

Set up the parts.

Three times a number:  \(\displaystyle 3x\)

Another number cubed:  \(\displaystyle y^3\)

The difference of three times a number and another number cubed:

\(\displaystyle 3x-y^3\)

The answer is:  \(\displaystyle 3x-y^3\)

Split the statement into parts.

Twice a number:  \(\displaystyle 2x\)

Ten more than twice a number:  \(\displaystyle 2x+10\)

The quantity of ten more than twice a number:  \(\displaystyle (2x+10)\)

The fourth root of the quantity of ten more than twice a number:

\(\displaystyle \sqrt[4]{2x+10}\)

The answer is:  \(\displaystyle \sqrt[4]{2x+10}\)

Break up the statement into parts in order to solve.

Twice a number:  \(\displaystyle 2x\)

Twice a number subtracted from eight:  \(\displaystyle 8-2x\)

The eight will take precedence since twice a number is subtracted from this number.

There is no need to add parentheses.

The answer is:  \(\displaystyle 8-2x\)

Break up the sentence into parts.  Start with the quantity first.

The square of a number:  \(\displaystyle x^2\)

Twice the square of a number:  \(\displaystyle 2x^2\)

Twice the square of a number less than three:  \(\displaystyle 3-2x^2\)

The fourth root of the quantity of:  \(\displaystyle \sqrt[4]{(...)}\)

Input the \(\displaystyle 3-2x^2\) term inside the fourth root.

The answer is:  \(\displaystyle \sqrt[4]{3-2x^2}\)

Natural log is the log that has a base of \(\displaystyle e\).  Do not confuse this with \(\displaystyle log()\) because this has a default base of \(\displaystyle 10\) unless the base is specified.

Twice a number:  \(\displaystyle 2x\)

The natural log of twice a number:  \(\displaystyle ln(2x)\)

Three more than the natural log of twice a number:  \(\displaystyle ln(2x)+3\)

The answer is:  \(\displaystyle ln(2x)+3\)