Solve (xz-(x-y)(y+z))-y(y-(x-z))

$$(xz-(x-y)(y+z))-y(y-(x-z))$$

Evaluate

$$0$$

Solution Steps

Apply the distributive property by multiplying each term of x-y by each term of y+z.

$$xz-\left(xy+xz-y^{2}-yz\right)-y\left(y-\left(x-z\right)\right)$$

To find the opposite of xy+xz-y^{2}-yz, find the opposite of each term.

$$xz-xy-xz-\left(-y^{2}\right)-\left(-yz\right)-y\left(y-\left(x-z\right)\right)$$

Combine xz and -xz to get 0.

$$-xy-\left(-y^{2}\right)-\left(-yz\right)-y\left(y-\left(x-z\right)\right)$$

The opposite of -y^{2} is y^{2}.

$$-xy+y^{2}-\left(-yz\right)-y\left(y-\left(x-z\right)\right)$$

The opposite of -yz is yz.

$$-xy+y^{2}+yz-y\left(y-\left(x-z\right)\right)$$

To find the opposite of x-z, find the opposite of each term.

$$-xy+y^{2}+yz-y\left(y-x-\left(-z\right)\right)$$

The opposite of -z is z.

$$-xy+y^{2}+yz-y\left(y-x+z\right)$$

Use the distributive property to multiply y by y-x+z.

$$-xy+y^{2}+yz-\left(y^{2}-yx+yz\right)$$

Combine -xy+y^{2}+yz and -\left(y^{2}-yx+yz\right) to get 0.

$$0$$

Factor

$$0$$