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