Write in Standard Form (4h^3+6h^2+1)-(5h^2-8h^4+6)

$(4 h^{3} + 6 h^{2} + 1) - (5 h^{2} - 8 h^{4} + 6)$

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

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

Simplify each term.

Apply the distributive property.

$4 h^{3} + 6 h^{2} + 1 - (5 h^{2}) - (- 8 h^{4}) - 1 \cdot 6$

Simplify.

Multiply $5$ by $- 1$ .

$4 h^{3} + 6 h^{2} + 1 - 5 h^{2} - (- 8 h^{4}) - 1 \cdot 6$

Multiply $- 8$ by $- 1$ .

$4 h^{3} + 6 h^{2} + 1 - 5 h^{2} + 8 h^{4} - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$4 h^{3} + 6 h^{2} + 1 - 5 h^{2} + 8 h^{4} - 6$

Simplify by adding terms.

Subtract $5 h^{2}$ from $6 h^{2}$ .

$4 h^{3} + h^{2} + 1 + 8 h^{4} - 6$

Simplify the expression.

Subtract $6$ from $1$ .

$4 h^{3} + h^{2} + 8 h^{4} - 5$

Move $h^{2}$ .

$4 h^{3} + 8 h^{4} + h^{2} - 5$

Reorder $4 h^{3}$ and $8 h^{4}$ .

$8 h^{4} + 4 h^{3} + h^{2} - 5$