Solve yx^2-5yx-50y

$$y { x }^{ 2 } -5yx-50y$$

Factor

$$y\left(x-10\right)\left(x+5\right)$$

Solution Steps

Factor out y.

$$y\left(x^{2}-5x-50\right)$$

Consider x^{2}-5x-50. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-50. To find a and b, set up a system to be solved.

$$a+b=-5 ab=1\left(-50\right)=-50$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -50.

$$1,-50 2,-25 5,-10$$

Calculate the sum for each pair.

$$1-50=-49 2-25=-23 5-10=-5$$

The solution is the pair that gives sum -5.

$$a=-10 b=5$$

Rewrite x^{2}-5x-50 as \left(x^{2}-10x\right)+\left(5x-50\right).

$$\left(x^{2}-10x\right)+\left(5x-50\right)$$

Factor out x in the first and 5 in the second group.

$$x\left(x-10\right)+5\left(x-10\right)$$

Factor out common term x-10 by using distributive property.

$$\left(x-10\right)\left(x+5\right)$$

Rewrite the complete factored expression.

$$y\left(x-10\right)\left(x+5\right)$$

Evaluate

$$y\left(x-10\right)\left(x+5\right)$$