Answer :
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]
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]
