Simplify (4a+x)(a-x)

$(4 a + x) (a - x)$

Step 1

Expand $(4 a + x) (a - x)$ using the FOIL Method.

Apply the distributive property.

$4 a (a - x) + x (a - x)$

Apply the distributive property.

$4 a \cdot a + 4 a (- x) + x (a - x)$

Apply the distributive property.

$4 a \cdot a + 4 a (- x) + x a + x (- x)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$4 (a \cdot a) + 4 a (- x) + x a + x (- x)$

Multiply $a$ by $a$ .

$4 a^{2} + 4 a (- x) + x a + x (- x)$

Rewrite using the commutative property of multiplication.

$4 a^{2} + 4 \cdot - 1 a x + x a + x (- x)$

Multiply $4$ by $- 1$ .

$4 a^{2} - 4 a x + x a + x (- x)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 4 a x + x a - x \cdot x$

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

Move $x$ .

$4 a^{2} - 4 a x + x a - (x \cdot x)$

Multiply $x$ by $x$ .

$4 a^{2} - 4 a x + x a - x^{2}$

Add $- 4 a x$ and $x a$ .

Reorder $x$ and $a$ .

$4 a^{2} - 4 a x + a x - x^{2}$

Add $- 4 a x$ and $a x$ .

$4 a^{2} - 3 a x - x^{2}$