Question 9 (Multiple Choice Worth 1 points) (07.04 MC) Which shows 42^2-38^2 being evaluated using the difference of perfect squares method? 42^2-38^2=(1,764-1,444)(1,764+1,444)=1,026,560 42^2-38^2=84-76=8 42^2-38^2=(42-38)^2=(4)^2=16 42^2-38^2=(42+38)(42-38)=(80)(4)=320

## Step 1<br />The problem asks us to identify which of the given options correctly evaluates \(42^{2}-38^{2}\) using the difference of squares method. The difference of squares method is a formula that states \(a^{2} - b^{2} = (a+b)(a-b)\).<br /><br />## Step 2<br />Let's evaluate each option:<br /><br />### Option 1: \(42^{2}-38^{2}=(1,764-1,444)(1,764+1,444)=1,026,560\)<br />This option incorrectly calculates the squares of 42 and 38 as 1764 and 1444 respectively, and then applies the difference of squares formula. However, the calculation of the squares is incorrect, and the application of the formula is also incorrect.<br /><br />### Option 2: \(42^{2}-38^{2}=84-76=8\)<br />This option incorrectly calculates the difference between 42 and 38 as 8, and then squares it. This is not the correct application of the difference of squares formula.<br /><br />### Option 3: \(42^{2}-38^{2}=(42-38)^{2}=(4)^{2}=16\)<br />This option incorrectly calculates the difference between 42 and 38 as 4, and then squares it. This is not the correct application of the difference of squares formula.<br /><br />### Option 4: \(42^{2}-38^{2}=(42+38)(42-38)=(80)(4)=320\)<br />This option correctly applies the difference of squares formula. It calculates the sum and difference of 42 and 38 as 80 and 4 respectively, and then multiplies these two results to get 320.