c) \( (x+11)^{2}= \) d) \( (9 x-8)(9 x+8)= \) e) \( (x-5)^{3}= \)

Let’s dive into some neat tricks for expanding these expressions! To expand \( (x+11)^{2} \), apply the formula \((a+b)^2 = a^2 + 2ab + b^2\). Here, \( a = x \) and \( b = 11 \). So, you get \( x^2 + 2(11)(x) + 11^2 = x^2 + 22x + 121 \). For \( (9x-8)(9x+8) \), you can use the difference of squares formula \( (a-b)(a+b) = a^2 - b^2 \). Here, \( a = 9x \) and \( b = 8 \). Therefore, \( (9x)^2 - 8^2 = 81x^2 - 64 \). Lastly, for \( (x-5)^{3} \), you can use the binomial expansion formula \((a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\). Plugging in \( a = x \) and \( b = 5 \) gives you \( x^3 - 3(5)x^2 + 3(5^2)x - 5^3 = x^3 - 15x^2 + 75x - 125 \).