Simplify x(a-x)(b+x)

$x (a - x) (b + x)$

Apply the distributive property.

$(x a + x (- x)) (b + x)$

Rewrite using the commutative property of multiplication.

$(x a - x \cdot x) (b + x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$(x a - (x \cdot x)) (b + x)$

Multiply $x$ by $x$ .

$(x a - x^{2}) (b + x)$

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

Apply the distributive property.

$x a (b + x) - x^{2} (b + x)$

Apply the distributive property.

$x a b + x a x - x^{2} (b + x)$

Apply the distributive property.

$x a b + x a x - x^{2} b - x^{2} x$

Simplify terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x a b + x \cdot x a - x^{2} b - x^{2} x$

Multiply $x$ by $x$ .

$x a b + x^{2} a - x^{2} b - x^{2} x$

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

Move $x$ .

$x a b + x^{2} a - x^{2} b - (x \cdot x^{2})$

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

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

$x a b + x^{2} a - x^{2} b - (x^{1} x^{2})$

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

$x a b + x^{2} a - x^{2} b - x^{1 + 2}$

Add $1$ and $2$ .

$x a b + x^{2} a - x^{2} b - x^{3}$

Simplify the expression.

Move $x$ .

$a b x + x^{2} a - x^{2} b - x^{3}$

Reorder $x^{2}$ and $a$ .

$a b x + a x^{2} - x^{2} b - x^{3}$

Move $x^{2}$ .

$a b x + a x^{2} - 1 b x^{2} - x^{3}$