Multiple Choice 10 points Which expression is equivalent to a^2-8a+16 (a+2)(a+8) (a+4)^2 (a+4)(a-4) (a-4)^2

To determine which expression is equivalent to \(a^2 - 8a + 16\), we need to factor or expand the given options and see which one matches the original expression.<br /><br />Let's start by expanding each option:<br /><br />1. \((a+2)(a+8)\):<br /> \[<br /> (a+2)(a+8) = a(a+8) + 2(a+8) = a^2 + 8a + 2a + 16 = a^2 + 10a + 16<br /> \]<br /> This does not match \(a^2 - 8a + 16\).<br /><br />2. \((a+4)^2\):<br /> \[<br /> (a+4)^2 = (a+4)(a+4) = a^2 + 4a + 4a + 16 = a^2 + 8a + 16<br /> \]<br /> This matches \(a^2 + 8a + 16\), but we need \(a^2 - 8a + 16\).<br /><br />3. \((a+4)(a-4)\):<br /> \[<br /> (a+4)(a-4) = a^2 - 4a + 4a - 16 = a^2 - 16<br /> \]<br /> This does not match \(a^2 - 8a + 16\).<br /><br />4. \((a-4)^2\):<br /> \[<br /> (a-4)^2 = (a-4)(a-4) = a^2 - 4a - 4a + 16 = a^2 - 8a + 16<br /> \]<br /> This matches \(a^2 - 8a + 16\).<br /><br />Therefore, the correct answer is:<br />\[<br />\boxed{(a-4)^2}<br />\]