Questions: Multiply. -5 a^2(2 a^2 - 5 a + 2) -5 a^2(2 a^2 - 5 a + 2) = (Simplify your answer.)

Solution Steps

To multiply the polynomial, distribute \(-5a^2\) to each term inside the parentheses. This involves multiplying \(-5a^2\) by each term separately and then combining the results.

We start with the expression: \[ -5a^{2}(2a^{2} - 5a + 2) \] To simplify, we distribute \(-5a^{2}\) to each term inside the parentheses.

Calculating each term:

• The first term: \(-5a^{2} \cdot 2a^{2} = -10a^{4}\)
• The second term: \(-5a^{2} \cdot (-5a) = 25a^{3}\)
• The third term: \(-5a^{2} \cdot 2 = -10a^{2}\)

Now, we combine the results from the multiplication: \[ -10a^{4} + 25a^{3} - 10a^{2} \]

Final Answer