Answer :
To solve the given problem of finding the total volume of two boxes, we need to combine their volumes by adding the expressions representing each box's volume. Here's how you can do that step by step:
1. Identify the Expressions:
- Volume of the first box: [tex]\( 84x^3 - 282x^2 - 138x - 336 \)[/tex]
- Volume of the second box: [tex]\( 27x^3 + 48x^2 - 99x \)[/tex]
2. Add the Expressions Together:
To find the total volume, you need to add these two expressions:
[tex]\[
(84x^3 - 282x^2 - 138x - 336) + (27x^3 + 48x^2 - 99x)
\][/tex]
3. Combine Like Terms:
- Combine the coefficients of [tex]\( x^3 \)[/tex]:
[tex]\[
84x^3 + 27x^3 = 111x^3
\][/tex]
- Combine the coefficients of [tex]\( x^2 \)[/tex]:
[tex]\[
-282x^2 + 48x^2 = -234x^2
\][/tex]
- Combine the coefficients of [tex]\( x \)[/tex]:
[tex]\[
-138x - 99x = -237x
\][/tex]
- The constant term remains the same as there is no constant term in the second expression to combine:
[tex]\[
-336
\][/tex]
4. Write the Resulting Expression:
After combining all the like terms, the expression for the total volume of the two boxes is:
[tex]\[
111x^3 - 234x^2 - 237x - 336
\][/tex]
This expression gives you the total volume of the two boxes when packed with the food collected during Shawn's school's canned food drive.
1. Identify the Expressions:
- Volume of the first box: [tex]\( 84x^3 - 282x^2 - 138x - 336 \)[/tex]
- Volume of the second box: [tex]\( 27x^3 + 48x^2 - 99x \)[/tex]
2. Add the Expressions Together:
To find the total volume, you need to add these two expressions:
[tex]\[
(84x^3 - 282x^2 - 138x - 336) + (27x^3 + 48x^2 - 99x)
\][/tex]
3. Combine Like Terms:
- Combine the coefficients of [tex]\( x^3 \)[/tex]:
[tex]\[
84x^3 + 27x^3 = 111x^3
\][/tex]
- Combine the coefficients of [tex]\( x^2 \)[/tex]:
[tex]\[
-282x^2 + 48x^2 = -234x^2
\][/tex]
- Combine the coefficients of [tex]\( x \)[/tex]:
[tex]\[
-138x - 99x = -237x
\][/tex]
- The constant term remains the same as there is no constant term in the second expression to combine:
[tex]\[
-336
\][/tex]
4. Write the Resulting Expression:
After combining all the like terms, the expression for the total volume of the two boxes is:
[tex]\[
111x^3 - 234x^2 - 237x - 336
\][/tex]
This expression gives you the total volume of the two boxes when packed with the food collected during Shawn's school's canned food drive.
