문자의 사용과 식의 계산

We need to be careful when an expression has a variable with an exponent. In this expression, $2{x}^{2}$ means $2\cdot x\cdot x$ and is different from the expression ${(2x)}^{2},$ which means $2x\cdot 2x.$

Simplify ${4}^{2}$.
Multiply.
Add.

40

9

The expression has four terms. They are $9b,15{x}^{2},a,$ and $6.$

The coefficient of $9b$ is $9.$

The coefficient of $15{x}^{2}$ is $15.$

Remember that if no number is written before a variable, the coefficient is $1.$ So the coefficient of $a$ is $1.$

The coefficient of a constant is the constant, so the coefficient of $6$ is $6.$

The terms are 4x, 3b, and 2. The coefficients are 4, 3, and 2.

The terms are 9a, 13a², and a³, The coefficients are 9, 13, and 1.

ⓐ $\,{y}^{3},7{x}^{2},14,23,4{y}^{3},9x,5{x}^{2}$

Look at the variables and exponents. The expression contains ${y}^{3},{x}^{2},x,$ and constants.

The terms ${y}^{3}$ and $4{y}^{3}$ are like terms because they both have ${y}^{3}.$

The terms $7{x}^{2}$ and $5{x}^{2}$ are like terms because they both have ${x}^{2}.$

The terms $14$ and $23$ are like terms because they are both constants.

The term $9x$ does not have any like terms in this list since no other terms have the variable $x$ raised to the power of $1.$

ⓑ $\,4{x}^{2}+2x+5{x}^{2}+6x+40x+8xy$

Look at the variables and exponents. The expression contains the terms $4{x}^{2},2x,5{x}^{2},6x,40x,\text{and}\,8xy$

The terms $4{x}^{2}$ and $5{x}^{2}$ are like terms because they both have ${x}^{2}.$

The terms $2x,6x,\text{and}\,40x$ are like terms because they all have $x.$

The term $8xy$ has no like terms in the given expression because no other terms contain the two variables $xy.$

9 and 15; 2x³ and 8x³; y² and 11y²

4x³ and 6x³; 8x² and 3x²; 19 and 24

16x + 17

17y + 7

Identify the like terms.
Rearrange the expression so like terms are together.
Add the coefficients of the like terms.

These are not like terms and cannot be combined. So $6{x}^{2}+4x$ is in simplest form.

4x² + 14x

12y² + 15y

ⓐ The key word is difference, which tells us the operation is subtraction. Look for the words of and and to find the numbers to subtract.

$\begin{array}{c} \\ \text{the difference}\,\text{of}\,20\,and\,4 \\ 20\,\text{minus}\,4 \\ 20-4\end{array}$

ⓑ The key word is quotient, which tells us the operation is division.

$\begin{array}{c} \\ \text{the quotient of}\,10x\,\text{and}\,3 \\ \text{divide}\,10x\,\text{by}\,3 \\ 10x\div 3\end{array}$

This can also be written as $\begin{array}{c}10x/3\,\text{or}\,\frac{10x}{3}\end{array}$

• ⓐ 47 − 41
• ⓑ 5x ÷ 2

• ⓐ 17 + 19
• ⓑ 7x

ⓐ The key words are more than. They tell us the operation is addition. More than means “added to”.

$\begin{array}{c}\text{Eight more than}\,y \\ \text{Eight added to}\,y \\ y+8\end{array}$

ⓑ The key words are less than. They tell us the operation is subtraction. Less than means “subtracted from”.

$\begin{array}{c}\text{Seven less than}\,9z \\ \text{Seven subtracted from}\,9z \\ 9z-7\end{array}$

• ⓐ x + 11
• ⓑ 11a − 14