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 $-6(1 -x^2)$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
