Do the following subtractions as directed.
Subtract $(3 x^{3} - 7 x + 4)$ from $(5 x^{3} + 7 x^{2} - 2 x)$

2 x^{3} + 4 x^{2} + 5 x - 2

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2 x^{3} + 7 x^{2} + 5 x - 2

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2 x^{3} + 7 x^{2} + 5 x - 4

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2 x^{3} + x^{2} + 5 x - 2

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Solution

The correct option is C $2 x^{3} + 7 x^{2} + 5 x - 4$
We know that Like terms are terms that contain the same variables raised to the same power.

We group together the like terms and subtract $3 x^{3} - 7 x + 4$ from $5 x^{3} + 7 x^{2} - 2 x$ as follows:

$(5 x^{3} + 7 x^{2} - 2 x) - (3 x^{3} - 7 x + 4) = 5 x^{3} + 7 x^{2} - 2 x - 3 x^{3} + 7 x - 4 = (5 x^{3} - 3 x^{3}) + 7 x^{2} + (- 2 x + 7 x) - 4 = 2 x^{3} + 7 x^{2} + 5 x - 4$

Hence, $(5 x^{3} + 7 x^{2} - 2 x) - (3 x^{3} - 7 x + 4) = 2 x^{3} + 7 x^{2} + 5 x - 4$ .

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