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Answer :
The equivalent expression to (3x⁶+2x³)-(x⁵-5x³) is 3x⁶ - x⁵ + 7x³, which is found by distributing the negative sign across the second polynomial and combining like terms. Therefore, the correct option is D.
The student has asked which expression is equivalent to the algebraic expression (3x⁶+2x³)-(x⁵-5x³). To solve this, we need to subtract the second polynomial from the first. This is done by distributing the negative sign to the terms in the second polynomial and then combining like terms.
Here is the step-by-step subtraction:
- Distribute the negative sign through the second polynomial: -1(x^5 - 5x^3) becomes -x^5 + 5x^3.
- Combine the like terms with the first polynomial: 3x^6 + 2x^3 - x^5 + 5x^3.
- Add the coefficients of like terms: 3x^6 (no like term) + -x^5 + (2x^3 + 5x^3) being 7x^3.
- The resulting expression is 3x^6 - x^5 + 7x^3, which matches option D.
Therefore, the equivalent expression is 3x^6 - x^5 + 7x^3.
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