Question

$-4x^2 + 8x$

Explanation:

Assuming the problem is to factor the expression \(-4x^2 + 8x\), here's the step - by - step solution:

Step 1: Identify the GCF

Find the greatest common factor (GCF) of the terms \(-4x^2\) and \(8x\). The GCF of \(-4\) and \(8\) is \(4\), and the GCF of \(x^2\) and \(x\) is \(x\). So the GCF of the two terms is \(4x\). But we can also factor out \(-4x\) for a neater form.

Step 2: Factor out the GCF

Factor out \(-4x\) from \(-4x^2+8x\). Using the distributive property \(ab + ac=a(b + c)\) (in reverse), we have:
\(-4x^2+8x=-4x\cdot x+(-4x)\cdot(- 2)=-4x(x - 2)\)

Answer:

\(-4x(x - 2)\) (or \(4x(-x + 2)\) is also correct, but \(-4x(x - 2)\) is a more standard factored form)