\( 2 x(-3 x y+4 x) \) Solution

To simplify \( 2 x(-3 x y + 4 x) \), first distribute \( 2x \) to each term inside the parentheses. You start with: \[ 2x \cdot (-3xy) + 2x \cdot (4x) \] This results in: \[ -6x^2y + 8x^2 \] So, the simplified expression is: \[ -6x^2y + 8x^2 \] Excellent work! Now, let's break it down a little further. Every time you see two polynomials being multiplied, it’s like throwing a party – everyone gets to dance, or in this case, every term gets to combine their movement (coefficients and variables) into a new form! Also, remember to look out for common factors in your final expression. In this case, both terms share a factor of \( 2x^2 \). Factoring that out can make it easier to work with in future equations! So you could express it as: \[ 2x^2(4 - 3y) \] This factors the expression nicely and reveals potential insights for solving equations or simplifying further later on. Cool, right?