Question

Expand $(x+1{)}^3$Using an Identity

Answer 1

Given: $(x+1{)}^3$

We know that ${(x+y)}^3=x^3+y^3+3xy(x+y).$

Now, substitute $y=1$ in the above formula, we get;

$\Rightarrow$${(x+1)}^3=x^3+1^3+3\left(x\right)\left(1\right)(x+1)$

$\Rightarrow$${(x+1)}^3=x^3+3x^2+3x+1.$

Hence, expansion of $(x+1{)}^3$is $x^3+3x^2+3x+1.$