To find the expressions that are equivalent to \(2x^2 - 8x - 10\) when distributed, we should expand each option and compare them to see which ones match the original expression.
Option #1: \(2x(x - 4x - 5)\)
Distributing gives:
\[
2x(x - 4x - 5) = 2x(-3x - 5) = -6x^2 - 10x \quad \text{(Not equivalent)}
\]
Option #2: \((2x + 2)(x - 5)\)
Distributing gives:
\[
(2x + 2)(x - 5) = 2x \cdot x - 2x \cdot 5 + 2 \cdot x - 2 \cdot 5 = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \quad \text{(Equivalent)}
\]
Option #3: \(2x(x - 5) + 2(x - 5)\)
Distributing gives:
\[
2x(x - 5) + 2(x - 5) = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \quad \text{(Equivalent)}
\]
Option #4: \((x - 5)(x - 3)\)
Distributing gives:
\[
(x - 5)(x - 3) = x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \quad \text{(Not equivalent)}
\]
Option #5: \(-6x - 10\)
This is a linear expression and does not match the original quadratic expression in any form.
\[
-6x - 10 \quad \text{(Not equivalent)}
\]
The only options that are equivalent to the original expression \(2x^2 - 8x - 10\) are Option #2 and Option #3.
Therefore, the answer is:
Option #___ and Option #___
Option #2 and Option #3
1 answer