Question

use the distributive property to remove the parentheses.
$4x^{2}\left(9x + 2x^{7}+6\
ight)$
simplify your answer as much as possible.

Explanation:

Step1: Distribute \(4x^2\) to \(9x\)

Using the distributive property \(a(b + c + d)=ab+ac + ad\), where \(a = 4x^2\), \(b=9x\), we get \(4x^2\times9x=36x^{2 + 1}=36x^3\)

Step2: Distribute \(4x^2\) to \(2x^7\)

For \(c = 2x^7\), we have \(4x^2\times2x^7=(4\times2)x^{2+7}=8x^9\)

Step3: Distribute \(4x^2\) to \(6\)

For \(d = 6\), we have \(4x^2\times6 = 24x^2\)

Step4: Combine the terms

Adding the results from Step1, Step2 and Step3, we get \(36x^3+8x^9 + 24x^2\). Rearranging the terms in descending order of exponents, we have \(8x^9+36x^3 + 24x^2\)

Answer:

\(8x^{9}+36x^{3}+24x^{2}\)