To simplify the given expression [tex]\(8 w^6 (5 w + 9 w^2)\)[/tex], we can follow these steps:
1. Distribute [tex]\(8 w^6\)[/tex] to each term inside the parenthesis:
[tex]\[
8 w^6 \cdot 5 w + 8 w^6 \cdot 9 w^2
\][/tex]
2. Multiply the coefficients and add the exponents for each term:
- For the first term [tex]\(8 w^6 \cdot 5 w\)[/tex]:
[tex]\[
8 \cdot 5 \cdot w^6 \cdot w^1 = 40 w^{6+1} = 40 w^7
\][/tex]
- For the second term [tex]\(8 w^6 \cdot 9 w^2\)[/tex]:
[tex]\[
8 \cdot 9 \cdot w^6 \cdot w^2 = 72 w^{6+2} = 72 w^8
\][/tex]
3. Combine the simplified terms to form the final expression:
[tex]\[
40 w^7 + 72 w^8
\][/tex]
4. Factor out the greatest common factor [tex]\(w^7\)[/tex] from both terms:
[tex]\[
w^7 (40 + 72 w)
\][/tex]
Therefore, the simplified form of the expression is:
[tex]\[
w^7 (40 + 72 w)
\][/tex]
