Questions: 1/5 x^2(20 x^2-10 x+2) 1/5 x^2(20 x^2-10 x+2)=

Solution Steps

To multiply the polynomial \(\frac{1}{5} x^{2}(20 x^{2}-10 x+2)\), distribute \(\frac{1}{5} x^{2}\) to each term inside the parentheses. This involves multiplying the coefficients and adding the exponents of like bases.

We start with the expression: \[ \frac{1}{5} x^{2}(20 x^{2}-10 x+2) \] To simplify, we distribute \(\frac{1}{5} x^{2}\) to each term inside the parentheses.

Calculating each term:

• For the first term: \[ \frac{1}{5} x^{2} \cdot 20 x^{2} = 4.0 x^{4} \]
• For the second term: \[ \frac{1}{5} x^{2} \cdot (-10 x) = -2.0 x^{3} \]
• For the third term: \[ \frac{1}{5} x^{2} \cdot 2 = 0.4 x^{2} \]

Combining all the terms gives us the expanded polynomial: \[ 4.0 x^{4} - 2.0 x^{3} + 0.4 x^{2} \]

Final Answer