Evaluate 5x^2-x(5x-3x(x-8)-11)+3

$5 x^{2} - x (5 x - 3 x (x - 8) - 11) + 3$

Simplify each term.

Apply the distributive property.

$5 x^{2} - x (5 x - 3 x \cdot x - 3 x \cdot - 8 - 11) + 3$

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

Move $x$ .

$5 x^{2} - x (5 x - 3 (x \cdot x) - 3 x \cdot - 8 - 11) + 3$

Multiply $x$ by $x$ .

$5 x^{2} - x (5 x - 3 x^{2} - 3 x \cdot - 8 - 11) + 3$

Multiply $- 8$ by $- 3$ .

$5 x^{2} - x (5 x - 3 x^{2} + 24 x - 11) + 3$

Add $5 x$ and $24 x$ .

$5 x^{2} - x (- 3 x^{2} + 29 x - 11) + 3$

Apply the distributive property.

$5 x^{2} - x (- 3 x^{2}) - x (29 x) - x \cdot - 11 + 3$

Simplify.

Rewrite using the commutative property of multiplication.

$5 x^{2} - 1 \cdot - 3 x \cdot x^{2} - x (29 x) - x \cdot - 11 + 3$

Rewrite using the commutative property of multiplication.

$5 x^{2} - 1 \cdot - 3 x \cdot x^{2} - 1 \cdot 29 x \cdot x - x \cdot - 11 + 3$

Multiply $- 11$ by $- 1$ .

$5 x^{2} - 1 \cdot - 3 x \cdot x^{2} - 1 \cdot 29 x \cdot x + 11 x + 3$

Simplify each term.

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

Move $x^{2}$ .

$5 x^{2} - 1 \cdot - 3 (x^{2} x) - 1 \cdot 29 x \cdot x + 11 x + 3$

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

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

$5 x^{2} - 1 \cdot - 3 (x^{2} x^{1}) - 1 \cdot 29 x \cdot x + 11 x + 3$

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

$5 x^{2} - 1 \cdot - 3 x^{2 + 1} - 1 \cdot 29 x \cdot x + 11 x + 3$

Add $2$ and $1$ .

$5 x^{2} - 1 \cdot - 3 x^{3} - 1 \cdot 29 x \cdot x + 11 x + 3$

Multiply $- 1$ by $- 3$ .

$5 x^{2} + 3 x^{3} - 1 \cdot 29 x \cdot x + 11 x + 3$

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

Move $x$ .

$5 x^{2} + 3 x^{3} - 1 \cdot 29 (x \cdot x) + 11 x + 3$

Multiply $x$ by $x$ .

$5 x^{2} + 3 x^{3} - 1 \cdot 29 x^{2} + 11 x + 3$

Multiply $- 1$ by $29$ .

$5 x^{2} + 3 x^{3} - 29 x^{2} + 11 x + 3$

Subtract $29 x^{2}$ from $5 x^{2}$ .

$3 x^{3} - 24 x^{2} + 11 x + 3$