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When the expression [tex][tex]$2x(x-4) - 3(x+5)$[/tex][/tex] is written in simplest form, the result is:

1. [tex][tex]$2x^2 - 11x - 15$[/tex][/tex]
2. [tex][tex]$2x^2 - 11x + 5$[/tex][/tex]
3. [tex][tex]$2x^2 - 3x - 19$[/tex][/tex]
4. [tex][tex]$2x^2 - 3x + 1$[/tex][/tex]

Sagot :

To write the given expression [tex]\(2x(x-4) - 3(x+5)\)[/tex] in simplest form, follow these steps:

1. Distribute the terms within each set of parentheses:
- For [tex]\(2x(x - 4)\)[/tex], distribute [tex]\(2x\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[ 2x \cdot x = 2x^2 \][/tex]
[tex]\[ 2x \cdot (-4) = -8x \][/tex]
So, [tex]\(2x(x - 4)\)[/tex] simplifies to [tex]\(2x^2 - 8x\)[/tex].

- For [tex]\(-3(x + 5)\)[/tex], distribute [tex]\(-3\)[/tex] to both [tex]\(x\)[/tex] and [tex]\(5\)[/tex]:
[tex]\[ -3 \cdot x = -3x \][/tex]
[tex]\[ -3 \cdot 5 = -15 \][/tex]
So, [tex]\(-3(x + 5)\)[/tex] simplifies to [tex]\(-3x - 15\)[/tex].

2. Combine the simplified parts:
[tex]\[ 2x^2 - 8x - 3x - 15 \][/tex]

3. Combine like terms:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -8x - 3x = -11x \][/tex]

- Thus, the expression becomes:
[tex]\[ 2x^2 - 11x - 15 \][/tex]

So, the simplified form of the given expression [tex]\(2x(x-4) - 3(x+5)\)[/tex] is:
[tex]\[ \boxed{2x^2 - 11x - 15} \][/tex]

Therefore, the correct answer is:
1) [tex]\(2x^2 - 11x - 15\)[/tex]
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