Q8. - Algebra 1

Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Identify the expression below that does not belong with the other two. Explain.

$\left(3m-2n\right)\left(3m+2n\right)$

$\left(3m+2n\right)\left(3m+2n\right)$

$\left(3m+2n\right)\left(3m-2n\right)$

Step-by-Step Solution

Answer

The expression that does not belong with the other two is $\left(3m+2n\right)\left(3m+2n\right)$ because the values of the expressions $\left(3m-2n\right)\left(3m+2n\right)$ and $\left(3m+2n\right)\left(3m-2n\right)$ are same equal to $9m^2-4n^2$ but the value of the expression $\left(3m+2n\right)\left(3m+2n\right)$ is $9m^2+12mn+4n^2$.

Step 1. Write the formula for a − b a + b and a + b 2 .

The formulas are:

 

$\left(a-b\right)\left(a+b\right)=a^2-b^2$

${\left(a+b\right)}^2=a^2+2ab+b^2$

Step 2. Identify the expression below that does not belong with the other two.

The value of the expression $\left(3m-2n\right)\left(3m+2n\right)$ is:

$$\begin{gathered} \left(3m-2n\right)\left(3m+2n\right)={\left(3m\right)}^2-{\left(2n\right)}^2\left(\because \left(a-b\right)\left(a+b\right)=a^2-b^2\right) \\ =3^2{m}^2-2^2{n}^2 \\ =9m^2-4n^2 \end{gathered}$$

The value of the expression $\left(3m+2n\right)\left(3m-2n\right)$ is:

$$\begin{gathered} \left(3m+2n\right)\left(3m-2n\right)={\left(3m\right)}^2-{\left(2n\right)}^2\left(\because \left(a-b\right)\left(a+b\right)=a^2-b^2\right) \\ =3^2{m}^2-2^2{n}^2 \\ =9m^2-4n^2 \end{gathered}$$

The value of the expression $\left(3m+2n\right)\left(3m+2n\right)$ is:

$$\begin{gathered} \left(3m+2n\right)\left(3m+2n\right)={\left(3m\right)}^2+2\left(3m\right)\left(2n\right)+{\left(2n\right)}^2\left(\because {\left(a+b\right)}^2=a^2+2ab+b^2\right) \\ =3^2{m}^2+12mn+2^2{n}^2 \\ =9m^2+12mn+4n^2 \end{gathered}$$

The expression that does not belong with the other two is $\left(3m+2n\right)\left(3m+2n\right)$ because the values of the expressions $\left(3m-2n\right)\left(3m+2n\right)$ and $\left(3m+2n\right)\left(3m-2n\right)$ are same equal to $9m^2-4n^2$ but the value of the expression $\left(3m+2n\right)\left(3m+2n\right)$ is $9m^2+12mn+4n^2$.