2.2 Evaluate, simplify, and translate expressions  (Page 2/9)

Solution

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

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

The coefficient of $15x^2$ 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 $6.$

Solution

ⓐ $y^3,7x^2,14,23,4y^3,9x,5x^2$

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

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

The terms $7x^2$ and $5x^2$ 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 $1.$

ⓑ $4x^2+2x+5x^2+6x+40x+8xy$

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

The terms $4x^2$ and $5x^2$ 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 $xy.$