Simplify 4x(x+1)-(3x-8)(x+4)

$4 x (x + 1) - (3 x - 8) (x + 4)$

Simplify each term.

Apply the distributive property.

$4 x \cdot x + 4 x \cdot 1 - (3 x - 8) (x + 4)$

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

Move $x$ .

$4 (x \cdot x) + 4 x \cdot 1 - (3 x - 8) (x + 4)$

Multiply $x$ by $x$ .

$4 x^{2} + 4 x \cdot 1 - (3 x - 8) (x + 4)$

Multiply $4$ by $1$ .

$4 x^{2} + 4 x - (3 x - 8) (x + 4)$

Apply the distributive property.

$4 x^{2} + 4 x + (- (3 x) - - 8) (x + 4)$

Multiply $3$ by $- 1$ .

$4 x^{2} + 4 x + (- 3 x - - 8) (x + 4)$

Multiply $- 1$ by $- 8$ .

$4 x^{2} + 4 x + (- 3 x + 8) (x + 4)$

Expand $(- 3 x + 8) (x + 4)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} + 4 x - 3 x (x + 4) + 8 (x + 4)$

Apply the distributive property.

$4 x^{2} + 4 x - 3 x \cdot x - 3 x \cdot 4 + 8 (x + 4)$

Apply the distributive property.

$4 x^{2} + 4 x - 3 x \cdot x - 3 x \cdot 4 + 8 x + 8 \cdot 4$

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$4 x^{2} + 4 x - 3 (x \cdot x) - 3 x \cdot 4 + 8 x + 8 \cdot 4$

Multiply $x$ by $x$ .

$4 x^{2} + 4 x - 3 x^{2} - 3 x \cdot 4 + 8 x + 8 \cdot 4$

Multiply $4$ by $- 3$ .

$4 x^{2} + 4 x - 3 x^{2} - 12 x + 8 x + 8 \cdot 4$

Multiply $8$ by $4$ .

$4 x^{2} + 4 x - 3 x^{2} - 12 x + 8 x + 32$

Add $- 12 x$ and $8 x$ .

$4 x^{2} + 4 x - 3 x^{2} - 4 x + 32$

Simplify by adding terms.

Combine the opposite terms in $4 x^{2} + 4 x - 3 x^{2} - 4 x + 32$ .

Subtract $4 x$ from $4 x$ .

$4 x^{2} - 3 x^{2} + 0 + 32$

Add $4 x^{2} - 3 x^{2}$ and $0$ .

$4 x^{2} - 3 x^{2} + 32$

Subtract $3 x^{2}$ from $4 x^{2}$ .

$x^{2} + 32$