+0

# Expand

0
25
1

Expand (sqrt(t) + 3t + 1)^3 + (sqrt(t) - 3t + 1)^3.

Jan 7, 2023

#1
+115
0

Alright, this is gonna be a long one.

first expand this whole thing

$$27t^3+36t^2+27t^2\sqrt{t}+19t\sqrt{t}+12t+3\sqrt{t}+1+\left(\sqrt{t}-3t+1\right)^3$$

$$=27t^3+36t^2+27t^2\sqrt{t}+19t\sqrt{t}+12t+3\sqrt{t}+1-27t^3+18t^2+27t^2\sqrt{t}-17t\sqrt{t}-6t+3\sqrt{t}+1$$

$$=27t^3-27t^3+36t^2+18t^2+27t^2\sqrt{t}+27t^2\sqrt{t}+19t\sqrt{t}-17t\sqrt{t}+12t-6t+3\sqrt{t}+3\sqrt{t}+1+1$$ grouping like terms

simplify to get: $$54t^2+54t^2\sqrt{t}+2t\sqrt{t}+6t+6\sqrt{t}+2$$

you technically could group them together in parenthesis and stuff but im not doing that

Jan 7, 2023