Simplify (x^3+8x^2)/(x^2+x-56)*(x^2-11x+28)/(4x)

Factor ${\displaystyle x^2}$ out of ${\displaystyle x^3}$.

Factor ${\displaystyle x^2}$ out of ${\displaystyle 8x^2}$.

Factor ${\displaystyle x^2}$ out of ${\displaystyle x^{2}x+x^2\cdot 8}$.

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 ${\displaystyle -56}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

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.

Combine.

Cancel the common factor of ${\displaystyle x^2}$ and ${\displaystyle x}$.

Cancel the common factor of ${\displaystyle x+8}$.

Cancel the common factor of ${\displaystyle x-7}$.