Structures of expressions unit test part 2 according to the distributive property which expression is equivalent to 4X power 3 + 8x ^ 2 + 12x?

Answer 1

To apply the distributive property and find an equivalent expression for \( 4x^3 + 8x^2 + 12x \), we can look for a common factor in all terms.

The common factor in the coefficients of \( 4, 8, \) and \( 12 \) is \( 4 \), and the lowest power of \( x \) across the terms is \( x \). Thus, we can factor out \( 4x \):

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

So, an expression equivalent to \( 4x^3 + 8x^2 + 12x \) is:

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