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Advanced Math / Equivalent expressions Difficulty: Medium

Which of the following is equivalent to the sum of $3 x to the fourth power, plus 2 x cubed$ and $4 x to the fourth power, plus 7 x cubed$ ?

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Explanation

Choice D is correct. Adding the two expressions yields $3 x to the fourth power, plus 2 x to the third power, plus 4 x to the fourth power, plus 7 x to the third power$ . Because the pair of terms $3 x to the fourth power$ and $4 x to the fourth power$ and the pair of terms $2 x to the third power$ and $7 x to the third power$ each contain the same variable raised to the same power, they are like terms and can be combined as $7 x to the fourth power$ and $9 x to the third power$ , respectively. The sum of the given expressions therefore simplifies to $7 x to the fourth power, plus 9 x to the third power$ .

Choice A is incorrect and may result from adding the coefficients and the exponents in the given expressions. Choice B is incorrect and may result from adding the exponents as well as the coefficients of the like terms in the given expressions. Choice C is incorrect and may result from multiplying, rather than adding, the coefficients of the like terms in the given expressions.