Question

simplify the expression
$6x^2(4x + 2) - 2x(5 - 4x)$

Explanation:

Step1: Distribute the terms

First, distribute \(6x^2\) into \((4x + 2)\) and \(-2x\) into \((5 - 4x)\).
For \(6x^2(4x + 2)\), we get \(6x^2\times4x + 6x^2\times2 = 24x^3 + 12x^2\).
For \(-2x(5 - 4x)\), we get \(-2x\times5 + (-2x)\times(-4x)= -10x + 8x^2\).
So the expression becomes \(24x^3 + 12x^2 - 10x + 8x^2\).

Step2: Combine like terms

Now, combine the like terms (the \(x^2\) terms).
\(12x^2 + 8x^2 = 20x^2\).
So the simplified expression is \(24x^3 + 20x^2 - 10x\).

Answer:

\(24x^3 + 20x^2 - 10x\)