Simplify (a-x)(x+a)

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

Expand $(a - x) (x + a)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$a x + a \cdot a - x \cdot x - x a$

Simplify terms.

Combine the opposite terms in $a x + a \cdot a - x \cdot x - x a$ .

Reorder the factors in the terms $a x$ and $- x a$ .

$a x + a \cdot a - x \cdot x - a x$

Subtract $a x$ from $a x$ .

$a \cdot a - x \cdot x + 0$

Add $a \cdot a - x \cdot x$ and $0$ .

$a \cdot a - x \cdot x$

Simplify each term.

Multiply $a$ by $a$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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