Question

multiply: $6x^2y^4(5x^2 - 3x^2y^2 + 4y^2)$
options:

• $11x^4y^4 + 3x^4y^6 + 10x^2y^6$
• $30x^4y^4 - 3x^2y^2 + 4y^2$
• $30x^4y^4 - 18x^4y^6 + 24x^2y^6$
• $30x^4y^4 - 18x^4y^8 + 24x^2y^8$

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.

Explanation:

Step1: Apply Distributive Property

Multiply \(6x^{2}y^{4}\) with each term inside the parentheses:
\(6x^{2}y^{4} \times 5x^{2}\), \(6x^{2}y^{4} \times (-3x^{2}y^{2})\), \(6x^{2}y^{4} \times 4y^{2}\).

Step2: Simplify each product using exponent rules (\(a^m \times a^n = a^{m+n}\))

• First term: \(6 \times 5 = 30\), \(x^{2} \times x^{2} = x^{4}\), \(y^{4}\) remains. So, \(30x^{4}y^{4}\).
• Second term: \(6 \times (-3) = -18\), \(x^{2} \times x^{2} = x^{4}\), \(y^{4} \times y^{2} = y^{6}\). So, \(-18x^{4}y^{6}\).
• Third term: \(6 \times 4 = 24\), \(x^{2}\) remains, \(y^{4} \times y^{2} = y^{6}\). So, \(24x^{2}y^{6}\).

Combine the terms: \(30x^{4}y^{4} - 18x^{4}y^{6} + 24x^{2}y^{6}\).

Answer:

The third option (from the left, labeled "30\(x^4y^4\) − 18\(x^4y^6\) + 24\(x^2y^6\)")