Questions: (8x^3+y^6)^2

Solution Steps

To solve the problem of multiplying \((8x^3 + y^6)^2\), we need to apply the binomial expansion formula. The expression is a binomial raised to the power of 2, which can be expanded using the formula \((a + b)^2 = a^2 + 2ab + b^2\). Here, \(a = 8x^3\) and \(b = y^6\).

1. Identify the terms \(a\) and \(b\) in the binomial.
2. Apply the binomial expansion formula: \((a + b)^2 = a^2 + 2ab + b^2\).
3. Calculate each term separately.

The given expression is \((8x^3 + y^6)^2\). Here, the terms of the binomial are \(a = 8x^3\) and \(b = y^6\).

To expand \((a + b)^2\), we use the formula: \[ (a + b)^2 = a^2 + 2ab + b^2 \]

• Calculate \(a^2\): \[ a^2 = (8x^3)^2 = 64x^6 \]
• Calculate \(2ab\): \[ 2ab = 2 \times 8x^3 \times y^6 = 16x^3y^6 \]
• Calculate \(b^2\): \[ b^2 = (y^6)^2 = y^{12} \]

Combine the calculated terms to get the expanded expression: \[ 64x^6 + 16x^3y^6 + y^{12} \]

Final Answer