Questions: Do Homework - R1.8 HW - Exponents and Order of Question 4, R1.8.15 Simplify the algebraic expression, or indicate that the expression cannot be simplified. 17 x^2 + 12 x^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. This cannot be simplified because the coefficients are different. B. This cannot be simplified because the coefficients are the same. C. This cannot be simplified because the variable factors of the terms are the same. D. 17 x^2 + 12 x^2 = □ (Simplify your answer.) E. This cannot be simplified because the variable factors of the terms are different.

Do Homework - R1.8 HW - Exponents and Order of Question 4, R1.8.15 Simplify the algebraic expression, or indicate that the expression cannot be simplified. 17 x^2 + 12 x^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. This cannot be simplified because the coefficients are different. B. This cannot be simplified because the coefficients are the same. C. This cannot be simplified because the variable factors of the terms are the same. D. 17 x^2 + 12 x^2 = □ (Simplify your answer.) E. This cannot be simplified because the variable factors of the terms are different.
Transcript text: Do Homework - R1.8 HW - Exp om/Student/PlayerHomework.aspx?homeworkld=690392621\&questionld=2\&flushed=false\& xponents and Order of Question 4, R1.8.15 Simplify the algebraic expression, or indicate that the expression cannot be simplified. \[ 17 x^{2}+12 x^{2} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. This cannot be simplified because the coefficients are different. B. This cannot be simplified because the coefficients are the same. C. This cannot be simplified because the variable factors of the terms are the same. D. $17 x^{2}+12 x^{2}=$ $\square$ (Simplify your answer.) E. This cannot be simplified because the variable factors of the terms are different. an example Get more help - Search
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Solution

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Solution Steps

Step 1: Identify Like Terms

The expression \(17x^{2} + 12x^{2}\) contains two terms with the same variable factor \(x^{2}\). These are called like terms.

Step 2: Combine Like Terms

Since the terms have the same variable factor, their coefficients can be added together: \[ 17x^{2} + 12x^{2} = (17 + 12)x^{2} \]

Step 3: Simplify the Coefficients

Add the coefficients \(17\) and \(12\): \[ 17 + 12 = 29 \] Thus, the simplified expression is: \[ 29x^{2} \]

Step 4: Select the Correct Choice

The correct choice is: D. \(17x^{2} + 12x^{2} =\) \(\boxed{29x^{2}}\)

Final Answer

D. \(17x^{2} + 12x^{2} = \boxed{29x^{2}}\)

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