Simplify 4x^2(2x^2+x-5)-x(x^3+5x^2-3)+17

$4 x^{2} (2 x^{2} + x - 5) - x (x^{3} + 5 x^{2} - 3) + 17$

Step 1

Simplify each term.

Apply the distributive property.

$4 x^{2} (2 x^{2}) + 4 x^{2} x + 4 x^{2} \cdot - 5 - x (x^{3} + 5 x^{2} - 3) + 17$

Simplify.

Rewrite using the commutative property of multiplication.

$4 \cdot 2 x^{2} x^{2} + 4 x^{2} x + 4 x^{2} \cdot - 5 - x (x^{3} + 5 x^{2} - 3) + 17$

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

Move $x$ .

$4 \cdot 2 x^{2} x^{2} + 4 (x \cdot x^{2}) + 4 x^{2} \cdot - 5 - x (x^{3} + 5 x^{2} - 3) + 17$

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

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

$4 \cdot 2 x^{2} x^{2} + 4 (x^{1} x^{2}) + 4 x^{2} \cdot - 5 - x (x^{3} + 5 x^{2} - 3) + 17$

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

$4 \cdot 2 x^{2} x^{2} + 4 x^{1 + 2} + 4 x^{2} \cdot - 5 - x (x^{3} + 5 x^{2} - 3) + 17$

Add $1$ and $2$ .

$4 \cdot 2 x^{2} x^{2} + 4 x^{3} + 4 x^{2} \cdot - 5 - x (x^{3} + 5 x^{2} - 3) + 17$

Multiply $- 5$ by $4$ .

$4 \cdot 2 x^{2} x^{2} + 4 x^{3} - 20 x^{2} - x (x^{3} + 5 x^{2} - 3) + 17$

Simplify each term.

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

Move $x^{2}$ .

$4 \cdot 2 (x^{2} x^{2}) + 4 x^{3} - 20 x^{2} - x (x^{3} + 5 x^{2} - 3) + 17$

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

$4 \cdot 2 x^{2 + 2} + 4 x^{3} - 20 x^{2} - x (x^{3} + 5 x^{2} - 3) + 17$

Add $2$ and $2$ .

$4 \cdot 2 x^{4} + 4 x^{3} - 20 x^{2} - x (x^{3} + 5 x^{2} - 3) + 17$

Multiply $4$ by $2$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - x (x^{3} + 5 x^{2} - 3) + 17$

Apply the distributive property.

$8 x^{4} + 4 x^{3} - 20 x^{2} - x \cdot x^{3} - x (5 x^{2}) - x \cdot - 3 + 17$

Simplify.

Multiply $x$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - (x^{3} x) - x (5 x^{2}) - x \cdot - 3 + 17$

Multiply $x^{3}$ by $x$ .

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

$8 x^{4} + 4 x^{3} - 20 x^{2} - (x^{3} x^{1}) - x (5 x^{2}) - x \cdot - 3 + 17$

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

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{3 + 1} - x (5 x^{2}) - x \cdot - 3 + 17$

Add $3$ and $1$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - x (5 x^{2}) - x \cdot - 3 + 17$

Rewrite using the commutative property of multiplication.

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 1 \cdot 5 x \cdot x^{2} - x \cdot - 3 + 17$

Multiply $- 3$ by $- 1$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 1 \cdot 5 x \cdot x^{2} + 3 x + 17$

Simplify each term.

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

Move $x^{2}$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 1 \cdot 5 (x^{2} x) + 3 x + 17$

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

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

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 1 \cdot 5 (x^{2} x^{1}) + 3 x + 17$

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

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 1 \cdot 5 x^{2 + 1} + 3 x + 17$

Add $2$ and $1$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 1 \cdot 5 x^{3} + 3 x + 17$

Multiply $- 1$ by $5$ .

$8 x^{4} + 4 x^{3} - 20 x^{2} - x^{4} - 5 x^{3} + 3 x + 17$

Step 2

Simplify by adding terms.

Subtract $x^{4}$ from $8 x^{4}$ .

$7 x^{4} + 4 x^{3} - 20 x^{2} - 5 x^{3} + 3 x + 17$

Subtract $5 x^{3}$ from $4 x^{3}$ .

$7 x^{4} - x^{3} - 20 x^{2} + 3 x + 17$

Simplify 4x^2(2x^2+x-5)-x(x^3+5x^2-3)+17

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