Simplify (x^2+11x+28)*(x+4)/(x+7)

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 28}$ and whose sum is ${\displaystyle 11}$.

Write the factored form using these integers.

Raise ${\displaystyle x+4}$ to the power of ${\displaystyle 1}$.

Raise ${\displaystyle x+4}$ to the power of ${\displaystyle 1}$.

Use the power rule ${\displaystyle a^m{a}^n=a^{m+n}}$ to combine exponents.

Add ${\displaystyle 1}$ and ${\displaystyle 1}$.

Cancel the common factor.

Divide ${\displaystyle {(x+4)}^2}$ by ${\displaystyle 1}$.

Multiply ${\displaystyle x}$ by ${\displaystyle x}$.

Move ${\displaystyle 4}$ to the left of ${\displaystyle x}$.

Multiply ${\displaystyle 4}$ by ${\displaystyle 4}$.