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: $3(1 - x^2)$
Correct Answer: $-6(1 - x^2)$
Solution : Given expression, $(1 + x)^3+ (1 - x)^3 + (-2)^3$ We know, $(a+b)^3=a^3+b^3+3a^2b+3ab^2$ And $(a-b)^3=a^3-b^3-3a^2b+3ab^2$ ⇒ $(1 + x)^3+ (1 - x)^3 + (-2)^3$ = $1+x^3+3(1)^2(x)+3(1)(x)^2+1-x^3-3(1)^2(x)+3(1)(x)^2-8$ = $1+x^3+3x+3x^2+1-x^3-3x+3x^2-8$ = $6x^2-6$ = $-6(1-x^2)$ Hence, the correct answer is $-6(1 -x^2)$.
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