(a+3)^2=(a-3)(b+3)=a^2+3a+3a+9=

Let's break down the given expression step by step:<br /><br />1. \((a+3)^2\):<br /> \[<br /> (a+3)^2 = (a+3)(a+3) = a^2 + 3a + 3a + 9 = a^2 + 6a + 9<br /> \]<br /><br />2. \((a-3)(b+3)\):<br /> \[<br /> (a-3)(b+3) = a(b+3) - 3(b+3) = ab + 3a - 3b - 9<br /> \]<br /><br />So, the expression \((a+3)^2 = (a-3)(b+3)\) is not correct because:<br />\[<br />a^2 + 6a + 9 \neq ab + 3a - 3b - 9<br />\]<br /><br />Therefore, the correct simplification of \((a+3)^2\) is:<br />\[<br />(a+3)^2 = a^2 + 6a + 9<br />\]<br /><br />And the expression \((a-3)(b+3)\) simplifies to:<br />\[<br />(a-3)(b+3) = ab + 3a - 3b - 9<br />\]<br /><br />These two expressions are not equal unless specific values for \(a\) and \(b\) are chosen such that the equality holds.