To simplify the expression \(7a^3(5a^6 - 2b^3)\), we can distribute \(7a^3\) across both terms inside the parentheses:

\[
7a^3(5a^6 - 2b^3) = 7a^3 \cdot 5a^6 - 7a^3 \cdot 2b^3
\]

Now, let's simplify each term:

1. First term: \(7a^3 \cdot 5a^6 = 35a^{3+6} = 35a^9\)
2. Second term: \(7a^3 \cdot 2b^3 = 14a^3b^3\)

Thus, the simplified expression is:

\[
35a^9 - 14a^3b^3
\]

Would you like any further details on this? Here are some related questions for practice:

1. Simplify \(4x^2(3x^4 + 5y^2)\).
2. Factor \(25a^9 - 5a^3b^3\).
3. Simplify \(8a^5b(3a^2 - 2b^3)\).
4. Expand \(2x^3(4x^2 - 7y)\).
5. Combine like terms in \(6a^9 + 3a^9 - a^3b^3\).

**Tip:** When distributing, remember to apply the power rule for exponents: \(a^m \cdot a^n = a^{m+n}\).

Learn how to simplify the algebraic expression 7a^3(5a^6 – 2b^3) using the distributive property and exponent rules. This step-by-step guide breaks down the multiplication and simplification process for polynomials, perfect for students in Grades 9-11.

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