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Simplified form of $3 x + 4 x − 2 + 2 x + 1 x − 1$ is

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5 x^{2} - 6 x - 9

4 x^{2} - 3 x - 9

5 x^{2} - 3 x - 9

5 x^{2} - 3 x - 7

answer is C.

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Detailed Solution

Given expression is

3 x + 4 x − 2 + 2 x + 1 x − 1

.
We know that binomials are multiplied using the distributive property of multiplication and like terms are combined.
Let us simplify first expression.
First expression =

3 x + 4 x − 2

3 x × x − 2 + 4 × x − 2

= 3 x 2 − 6 x + 4 x − 8

= 3 x 2 − 2 x − 8

---(1) Now, let us simplify second expression
Second expression =

2 x + 1 x − 1

2 x × x − 1 + 1 × x − 1

= 2 x 2 − 2 x + x − 1

= 2 x 2 − x − 1

---(2)
Now to get the sum of the given whole expression, add the simplified expressions (1) and (2).

3 x + 4 x − 2 + 2 x + 1 x − 1

= 3 x 2 − 2 x − 8 + 2 x 2 − x − 1

= 5 x 2 − 3 x − 9

So,

3 x + 4 x − 2 + 2 x + 1 x − 1 = 5 x 2 − 3 x − 9

The correct option is (3).

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