Question

1. distribute the multiplication and simplify $2x(8x^2 + 3x - 5)$

$2x(8x^2 + 3x - 5) = $ enter your next step here

Explanation:

Step1: Distribute 2x to each term

Using the distributive property \(a(b + c + d)=ab+ac + ad\), here \(a = 2x\), \(b=8x^{2}\), \(c = 3x\), \(d=- 5\). So we get \(2x\times8x^{2}+2x\times3x+2x\times(-5)\)

Step2: Simplify each product

For \(2x\times8x^{2}\), using the rule \(x^{m}\times x^{n}=x^{m + n}\), we have \(2\times8\times x^{1+2}=16x^{3}\). For \(2x\times3x\), we get \(2\times3\times x^{1 + 1}=6x^{2}\). For \(2x\times(-5)\), we get \(-10x\). Then combine them: \(16x^{3}+6x^{2}-10x\)

Answer:

\(16x^{3}+6x^{2}-10x\)