Question

(10) select all the correct way factoring -2y -8
2(x - 4) 2(-x - 4)
-2(x + 4) -2(-x - 4)
2(x + 4)

Explanation:

Step1: Recall the distributive property

The distributive property is \(a(b + c)=ab+ac\). We need to factor out \(-2\) from \(-2y - x\) (assuming there's a typo and it's \(-2x - y\) or similar, but looking at the options, let's assume the expression is \(-2x - y\)? Wait, the original problem says "factoring \(-2y - x\)"? Wait, maybe it's \(-2x - y\) or the options are for factoring \(-2x - 4\)? Wait, looking at the options: \(2(x - 4)\), \(2(-x - 4)\), \(-2(x + 4)\), \(-2(-x - 4)\), \(2(x + 4)\). Wait, maybe the expression to factor is \(-2x - 8\)? Wait, let's check each option:

Let's take the expression as \(-2x - 8\) (maybe a typo in the original, since \(-2y - x\) doesn't match the options. Let's assume the correct expression is \(-2x - 8\)).

Step2: Factor each option:

• For \(2(x - 4)\): Distribute \(2\): \(2x-8\), not \(-2x - 8\).
• For \(2(-x - 4)\): Distribute \(2\): \(2\times(-x)+2\times(-4)=-2x - 8\). Correct.
• For \(-2(x + 4)\): Distribute \(-2\): \(-2x-8\). Correct.
• For \(-2(-x - 4)\): Distribute \(-2\): \(2x + 8\), not \(-2x - 8\).
• For \(2(x + 4)\): Distribute \(2\): \(2x + 8\), not \(-2x - 8\).

Wait, maybe the original expression is \(-2x - 8\). So the correct ways to factor \(-2x - 8\) are:

• \(2(-x - 4)\): \(2\times(-x)+2\times(-4)=-2x - 8\)
• \(-2(x + 4)\): \(-2\times x+(-2)\times4=-2x - 8\)

Let's verify:

For \(2(-x - 4)\):
\(2\times(-x)+2\times(-4)=-2x - 8\), which matches if the expression is \(-2x - 8\).

For \(-2(x + 4)\):
\(-2\times x+(-2)\times4=-2x - 8\), which also matches.

Answer:

The correct options are \(2(-x - 4)\) and \(-2(x + 4)\) (assuming the expression to factor is \(-2x - 8\) due to the options provided). If we take the original as \(-2x - 8\), then:

• \(2(-x - 4)\) (distribute \(2\): \(2\times(-x)+2\times(-4)=-2x - 8\))
• \(-2(x + 4)\) (distribute \(-2\): \(-2x-8\))