Question

the movement of the progress bar may be uneven because questions can be worth more or less multiply: $2x^{3}y^{2}\left(3x^{2}-5x^{2}y^{2}+4y^{2}\
ight)$ $\bigcirc\\ 6x^{6}y^{2}-10x^{6}y^{4}+8x^{3}y^{4}$ $\bigcirc\\ 6x^{5}y^{2}-5x^{2}y^{2}+4y^{2}$ $\bigcirc\\ 5x^{5}y^{2}-3x^{5}y^{4}+6x^{3}y^{4}$ $\bigcirc\\ 6x^{5}y^{2}-10x^{5}y^{4}+8x^{3}y^{4}$

Explanation:

Step1: Distribute \(2x^3y^2\) to \(3x^2\)

Using the rule \(a^m \cdot a^n = a^{m + n}\), we have \(2x^3y^2 \cdot 3x^2 = (2 \cdot 3)x^{3 + 2}y^2 = 6x^5y^2\).

Step2: Distribute \(2x^3y^2\) to \(-5x^2y^2\)

Applying the same exponent rule, \(2x^3y^2 \cdot (-5x^2y^2) = (2 \cdot (-5))x^{3 + 2}y^{2 + 2} = -10x^5y^4\).

Step3: Distribute \(2x^3y^2\) to \(4y^2\)

Using the exponent rule for multiplication, \(2x^3y^2 \cdot 4y^2 = (2 \cdot 4)x^3y^{2 + 2} = 8x^3y^4\).

Step4: Combine the results

Putting it all together, we get \(6x^5y^2 - 10x^5y^4 + 8x^3y^4\).

Answer:

\(6x^5y^2 - 10x^5y^4 + 8x^3y^4\) (the last option: \(6x^5y^2 - 10x^5y^4 + 8x^3y^4\))