Find the sum.
$17 x^3+\left(3 x+8 x^3\right)=$
A. $28 x^3$
B. $28 x^7$
C. $25 x^3+3 x$
D. $26 x^3+3 x$
Answer (2)
Remove the parentheses: 17 x 3 + ( 3 x + 8 x 3 ) = 17 x 3 + 3 x + 8 x 3 .
Combine the x 3 terms: 17 x 3 + 8 x 3 = 25 x 3 .
Write the simplified expression: 25 x 3 + 3 x .
The final answer is: 25 x 3 + 3 x .
Explanation
Understanding the Problem We are asked to find the sum of the expression 17 x 3 + ( 3 x + 8 x 3 ) . This involves combining like terms to simplify the expression.
Removing Parentheses First, remove the parentheses: 17 x 3 + ( 3 x + 8 x 3 ) = 17 x 3 + 3 x + 8 x 3
Grouping Like Terms Next, group the like terms together. In this case, we have two terms with x 3 and one term with x : ( 17 x 3 + 8 x 3 ) + 3 x
Combining Like Terms Now, combine the like terms by adding their coefficients: 17 x 3 + 8 x 3 = ( 17 + 8 ) x 3 = 25 x 3 So the expression becomes: 25 x 3 + 3 x
Final Answer Therefore, the simplified expression is 25 x 3 + 3 x . Comparing this to the given options, we see that it matches option C.
Examples
Understanding how to combine like terms is fundamental in many areas, such as calculating the total cost of items. For example, if you buy 17 items costing x 3 dollars each and another 8 items costing x 3 dollars each, plus an additional 3 items costing x dollars each, the total cost would be ( 17 x 3 + 8 x 3 + 3 x ) dollars, which simplifies to ( 25 x 3 + 3 x ) dollars. This skill is also useful in physics, where you might combine terms representing similar physical quantities to simplify equations.
The sum of the expression 17 x 3 + ( 3 x + 8 x 3 ) simplifies to 25 x 3 + 3 x . The correct option is C: 25 x 3 + 3 x .
;
