Question

1. simplify and write your answer in standard form.

$3x\left(-4x + 2x^{3} + 5 + 3x^{2}\
ight)$
type a response

Explanation:

Step1: Distribute \(3x\) to each term

Using the distributive property \(a(b + c + d + e)=ab+ac+ad+ae\), we have:
\(3x\times(-4x)+3x\times2x^{3}+3x\times5 + 3x\times3x^{2}\)

Step2: Simplify each term

• For \(3x\times(-4x)\): Using the rule \(x^{m}\times x^{n}=x^{m + n}\), we get \(-12x^{2}\).
• For \(3x\times2x^{3}\): We get \(6x^{4}\).
• For \(3x\times5\): We get \(15x\).
• For \(3x\times3x^{2}\): We get \(9x^{3}\).

So the expression becomes \(6x^{4}+9x^{3}-12x^{2}+15x\) (arranged in standard form, descending powers of \(x\)).

Answer:

\(6x^{4}+9x^{3}-12x^{2}+15x\)