according to the distributive property, which expression is equivalent 4x^3 + 8x^2 + 12x?

Answer 1

The distributive property states that \( a(b + c) = ab + ac \). To apply this property to the expression \( 4x^3 + 8x^2 + 12x \), we can factor out the greatest common factor (GCF) of the terms.

In this case, the GCF of \( 4x^3 \), \( 8x^2 \), and \( 12x \) is \( 4x \).

So, we can factor \( 4x \) out of the expression:

\[ 4x^3 + 8x^2 + 12x = 4x(x^2 + 2x + 3) \]

Therefore, an equivalent expression using the distributive property is:

\[ 4x(x^2 + 2x + 3) \]