Question : Simplify the given expression: $(1 + x)^3 + (1 – x)^3 + (–2)^3$

Option 1: $6(1 - x^2)$

Option 2: $-3(1 - x^2)$

Option 3: $-6(1 - x^2)$

Option 4: $3(1 - x^2)$

Question : Simplify the given expression.
$(1 - 2x)^2 - (1 + 2x)^2$

Option 1: $8x$

Option 2: $-8x$

Option 3: $-(2 + 8x^2)$

Option 4: $2 + 8x^2$

Question : If 2A = 3B and 3B = 2C, then what is $A:B:C$?

Option 1: $3:2:3$

Option 2: $2:3:2$

Option 3: $1:3:1$

Option 4: $2:3:4$

Question : If $2A=3B$, then what is the value of $\frac{A+B}{A}$?

Option 1: $\frac{5}{4}$

Option 2: $\frac{2}{3}$

Option 3: $\frac{5}{2}$

Option 4: $\frac{5}{3}$

Question : If $\left (2a-3 \right )^{2}+\left (3b+4 \right )^{2}+\left ( 6c+1\right)^{2}=0$, then the value of $\frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}}+3$ is:

Option 1: $abc+3$

Option 2: $6$

Option 3: $0$

Option 4: $3$