Perform the indicated operation. Simplify, if possible. $( 4 \sqrt { 3 } - 1 ) ^ { 2 }$
A) 49
B) $49 - 8 \sqrt { 3 }$
C) $49 - 4 \sqrt { 3 }$
D) -72

Question

Quizplus · Accepted Answer

To solve $(4\sqrt{3} - 1)^2$, we apply the formula $(a - b)^2 = a^2 - 2ab + b^2$, where $a = 4\sqrt{3}$ and $b = 1$. Thus, $a^2 = (4\sqrt{3})^2 = 16*3 = 48$, $2ab = 2*(4\sqrt{3})*1 = 8\sqrt{3}$, and $b^2 = 1^2 = 1$. Adding these together, we get $48 - 8\sqrt{3} + 1 = 49 - 8\sqrt{3}$.

Perform the Indicated Operation (43−1)2( 4 \sqrt { 3 } - 1 ) ^ { 2 }(43​−1)2

Perform the Indicated Operation $( 4 \sqrt { 3 } - 1 ) ^ { 2 }$