Find the product. (8x+3)^3 (8x+3)^3= square

To find the product \((8x + 3)^3\), we need to expand it using the binomial theorem or by multiplying it out step by step.<br /><br />The binomial theorem states that:<br /><br />\[<br />(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k<br />\]<br /><br />For \((8x + 3)^3\), we have \(a = 8x\), \(b = 3\), and \(n = 3\). Applying the binomial theorem, we get:<br /><br />\[<br />(8x + 3)^3 = \sum_{k=0}^{3} \binom{3}{k} (8x)^{3-k} (3)^k<br />\]<br /><br />Calculating each term:<br /><br />1. For \(k = 0\):<br /> \[<br /> \binom{3}{0} (8x)^3 (3)^0 = 1 \cdot (8x)^3 \cdot 1 = 512x^3<br /> \]<br /><br />2. For \(k = 1\):<br /> \[<br /> \binom{3}{1} (8x)^2 (3)^1 = 3 \cdot 64x^2 \cdot 3 = 576x^2<br /> \]<br /><br />3. For \(k = 2\):<br /> \[<br /> \binom{3}{2} (8x)^1 (3)^2 = 3 \cdot 8x \cdot 9 = 216x<br /> \]<br /><br />4. For \(k = 3\):<br /> \[<br /> \binom{3}{3} (8x)^0 (3)^3 = 1 \cdot 1 \cdot 27 = 27<br /> \]<br /><br />Adding all these terms together, we get:<br /><br />\[<br />(8x + 3)^3 = 512x^3 + 576x^2 + 216x + 27<br />\]<br /><br />Thus, the expanded form of \((8x + 3)^3\) is:<br /><br />\[<br />512x^3 + 576x^2 + 216x + 27<br />\]