Question

when the expression $2x(x - 4) - 3(x + 5)$ is written in simplest form, the result is

1. $2x^2 - 11x - 15$
2. $2x^2 - 11x + 5$
3. $2x^2 - 3x - 19$
4. $2x^2 - 3x + 1$

Explanation:

Step1: Expand the terms

First, expand \(2x(x - 4)\) using the distributive property (\(a(b - c)=ab - ac\)):
\(2x(x - 4)=2x\cdot x - 2x\cdot 4 = 2x^{2}-8x\).

Then, expand \(-3(x + 5)\) using the distributive property (\(a(b + c)=ab + ac\)):
\(-3(x + 5)=-3\cdot x+(-3)\cdot 5=-3x - 15\).

Step2: Combine the expanded terms

Now, combine the two expanded expressions:
\(2x^{2}-8x-3x - 15\).

Step3: Combine like terms

Combine the \(x\)-terms (\(-8x - 3x\)):
\(-8x-3x=-11x\).

So the simplified expression is \(2x^{2}-11x - 15\).

Answer:

1. \(2x^{2}-11x - 15\)