Question

find the product.
\\((a^2)(2a^3)(a^2 - 8a + 9)\\)

\\(2a^7 - 16a^6 + 18a^5\\)
\\(2a^7 - 16a^6 - 18a^5\\)
\\(2a^8 - 16a^7 + 18a^6\\)
\\(2a^{12} - 16a^7 + 18a^6\\)

Explanation:

Multiply the monomials

$$ (a^2)(2a^3) = 2a^{2+3} = 2a^5 $$

Distribute over the trinomial

$$ 2a^5(a^2 - 8a + 9) = (2a^5)(a^2) - (2a^5)(8a) + (2a^5)(9) $$

Simplify each term

$$ 2a^7 - 16a^6 + 18a^5 $$

Answer:

• (A) \(2a^7 - 16a^6 + 18a^5\) (Correct answer)
• (B) \(2a^7 - 16a^6 - 18a^5\)
• (C) \(2a^8 - 16a^7 + 18a^6\)
• (D) \(2a^{12} - 16a^7 + 18a^6\)