Expand and combine like terms. (2a^6-6a^3)^2=

To expand and combine like terms for the expression \((2a^{6}-6a^{3})^{2}\), we can use the binomial theorem or apply the formula \((a-b)^2 = a^2 - 2ab + b^2\).<br /><br />Let's rewrite the expression:<br />\[<br />(2a^{6}-6a^{3})^{2}<br />\]<br /><br />Using the binomial formula \((a-b)^2 = a^2 - 2ab + b^2\), where \(a = 2a^6\) and \(b = 6a^3\):<br /><br />\[<br />(2a^6 - 6a^3)^2 = (2a^6)^2 - 2(2a^6)(^3) + (6a^3)^2<br />\]<br /><br />Now, calculate each term separately:<br /><br />1. \((2a^6)^2 = 4a^{12}\)<br />2. \(2(2a^6)(6a^3) = 2 \cdot 2 \cdot 6 \cdot a^6 \cdot a^3 = 24a^9\)<br />3. \((6a^3)^2 = 36a^6\)<br /><br />Putting it all together:<br /><br />\[<br />(2a^6 - 6a^3)^2 = 4a^{12} - 24a^9 + 36a^6<br />\]<br /><br />So, the expanded and combined form of the expression is:<br /><br />\[<br />4a^{12} - 24a^9 + 36a^6<br />\]