Write in Standard Form 4x^2(-2x^2+5x^3)

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $4$ by $- 2$ .

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

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

$- 8 x^{4} + 4 \cdot 5 x^{5}$

Multiply $4$ by $5$ .

$- 8 x^{4} + 20 x^{5}$

Step 4

Reorder $- 8 x^{4}$ and $20 x^{5}$ .

$20 x^{5} - 8 x^{4}$