Simplify (x^2+z)(x^3-xz)

$(x^{2} + z) (x^{3} - x z)$

Step 1

Expand $(x^{2} + z) (x^{3} - x z)$ using the FOIL Method.

Apply the distributive property.

$x^{2} (x^{3} - x z) + z (x^{3} - x z)$

Apply the distributive property.

$x^{2} x^{3} + x^{2} (- x z) + z (x^{3} - x z)$

Apply the distributive property.

$x^{2} x^{3} + x^{2} (- x z) + z x^{3} + z (- x z)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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

$x^{2 + 3} + x^{2} (- x z) + z x^{3} + z (- x z)$

Add $2$ and $3$ .

$x^{5} + x^{2} (- x z) + z x^{3} + z (- x z)$

Rewrite using the commutative property of multiplication.

$x^{5} - x^{2} (x z) + z x^{3} + z (- x z)$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$x^{5} - (x \cdot x^{2}) z + z x^{3} + z (- x z)$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{5} - (x^{1} x^{2}) z + z x^{3} + z (- x z)$

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

$x^{5} - x^{1 + 2} z + z x^{3} + z (- x z)$

Add $1$ and $2$ .

$x^{5} - x^{3} z + z x^{3} + z (- x z)$

Rewrite using the commutative property of multiplication.

$x^{5} - x^{3} z + z x^{3} - z (x z)$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$x^{5} - x^{3} z + z x^{3} - (z \cdot z) x$

Multiply $z$ by $z$ .

$x^{5} - x^{3} z + z x^{3} - z^{2} x$

Add $- x^{3} z$ and $z x^{3}$ .

Reorder $z$ and $x^{3}$ .

$x^{5} - x^{3} z + x^{3} z - z^{2} x$

Add $- x^{3} z$ and $x^{3} z$ .

$x^{5} + 0 - z^{2} x$

Add $x^{5}$ and $0$ .

$x^{5} - z^{2} x$