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The expression [tex]\left(5 x^2 - x + 4\right) - 3\left(x^2 - x - 2\right)[/tex] is equivalent to:

1. [tex]2 x^2 - 2 x + 2[/tex]

2. [tex]2 x^2 + 2 x + 10[/tex]

3. [tex]2 x^4 - 2 x^2 + 2[/tex]

4. [tex]2 x^4 - 2 x^2 + 10[/tex]

Sagot :

GinnyAnsweridn
To determine which option the expression [tex]\(\left(5 x^2 - x + 4\right) - 3\left(x^2 - x - 2\right)\)[/tex] is equivalent to, we need to simplify it step-by-step.

Let's begin by expanding and simplifying the given expression:

1. Distribute the terms within each bracket:

[tex]\[ \left(5 x^2 - x + 4\right) - 3\left(x^2 - x - 2\right) \][/tex]

First, expand the second part of the expression by distributing the -3 to each term inside the parentheses:

[tex]\[ -3(x^2 - x - 2) = -3 \cdot x^2 + 3 \cdot x + 3 \cdot 2 = -3x^2 + 3x + 6 \][/tex]

2. Rewrite the expression with this expansion:

[tex]\[ \left(5 x^2 - x + 4\right) - 3x^2 + 3x + 6 \][/tex]

3. Combine like terms:

Let's group together the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms:

[tex]\[ 5x^2 - 3x^2 = 2x^2 \][/tex]

[tex]\[ -x + 3x = 2x \][/tex]

[tex]\[ 4 + 6 = 10 \][/tex]

4. Combine the simplified terms:

[tex]\[ 2x^2 + 2x + 10 \][/tex]

This final expression is [tex]\(2x^2 + 2x + 10\)[/tex].

Therefore, the correct option is:
(2) [tex]\(2 x^2 + 2 x + 10\)[/tex]
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