Chapter 11.7, Problem 1WE

To determine

To calculate:

The expansion and simplification of the expression.

  ${\left(x+y\right)}^3$

Answer to Problem 1WE

The simplified expression is $x^3+3x^{2}y+3x{y}^2+y^3$ .

Explanation of Solution

Given information:

  ${\left(x+y\right)}^3$

Formula:

The formula of cube ${\left(a+b\right)}^3$ is given by,

  ${\left(a+b\right)}^3=a^3+3a^{2}b+3a{b}^{2}2+b^3$

Calculation:

The expression given is,

  ${\left(x+y\right)}^3$

Consider $\begin{array}{l}a=x\\ b=y\end{array}$

Now here by using the formula of expansion, expand the above expression.

Put $a=x,b=y$ in the formula.

  ${\left(a+b\right)}^3=a^3+3a^{2}b+3a{b}^{2}2+b^3$

By substituting in the formula the expression where $a=x,b=y$ is thus written as,

  ${\left(x+y\right)}^3=x^3+3x^{2}y+3x{y}^2+y^3$