Chapter 6.8, Problem 15SGR

To determine

To calculate: The simplification of the expression $\left(m+p\right)\left(m^2-2mp+p^2\right)$ and consider that no variable is equal to 0.

Answer to Problem 15SGR

The simplification of expression $\left(m+p\right)\left(m^2-2mp+p^2\right)$ is $m^3-m^{2}p-m{p}^2+p^3$ .

Explanation of Solution

Given information:

The expression is given as:

  $\left(m+p\right)\left(m^2-2mp+p^2\right)$

Formula used:

Distributive property:

If multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

Calculation:

Consider the expression,

  $\left(m+p\right)\left(m^2-2mp+p^2\right)$

By the distributive property,

  $\left(m\right)\left(m^2-2mp+p^2\right)+\left(p\right)\left(m^2-2mp+p^2\right)$

Multiply monomials as,

  $m^3-2m^{2}p+m{p}^2+m^{2}p-2m{p}^2+p^3$

Now, solve further $m^3-m^{2}p-m{p}^2+p^3$

Thus, the expression can be written as $m^3-m^{2}p-m{p}^2+p^3$ .