(a³-b⁴) ²

To simplify \((a^3 - b^4)^2\), we can use the formula for the square of a binomial, which states that \((x - y)^2 = x^2 - 2xy + y^2\). Here, let \(x = a^3\) and \(y = b^4\). Applying the formula, we get: \[ (a^3 - b^4)^2 = (a^3)^2 - 2(a^3)(b^4) + (b^4)^2 \] Now, calculate each term: 1. \((a^3)^2 = a^{3 \cdot 2} = a^6\) 2. \((b^4)^2 = b^{4 \cdot 2} = b^8\) 3. \(-2(a^3)(b^4) = -2a^3b^4\) Putting it all together: \[ (a^3 - b^4)^2 = a^6 - 2a^3b^4 + b^8 \] So the final result is: \[ a^6 - 2a^3b^4 + b^8 \]