Do the following subtractions as directed.
Subtract the sum of $(a^{2} - 3 a)$ and $7$ from the sum of $3 a^{2}$ and $2 a - 2$

4 a^{2} + 5 a + 9

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2 a^{2} + 5 a - 9

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- 2 a^{2} + 5 a + 9

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4 a^{2} - 5 a + 9

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Solution

The correct option is A $2 a^{2} + 5 a - 9$
The sum of $a^{2} - 3 a$ and $7$ is $a^{2} - 3 a + 7$ and the sum of $3 a^{2}$ and $2 a - 2$ is $3 a^{2} + 2 a - 2$ .

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 $a^{2} - 3 a + 7$ from $3 a^{2} + 2 a - 2$ as follows:

$(3 a^{2} + 2 a - 2) - (a^{2} - 3 a + 7) = 3 a^{2} + 2 a - 2 - a^{2} + 3 a - 7 = (3 a^{2} - a^{2}) + (2 a + 3 a) + (- 2 - 7) = 2 a^{2} + 5 a - 9$

Hence, $(3 a^{2} + 2 a - 2) - (a^{2} - 3 a + 7) = 2 a^{2} + 5 a - 9$ .

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