Simplify (7x^2-4x-3)-(9x^3+4x^2-9x+1)

$(7 x^{2} - 4 x - 3) - (9 x^{3} + 4 x^{2} - 9 x + 1)$

Step 1

Simplify each term.

Apply the distributive property.

$7 x^{2} - 4 x - 3 - (9 x^{3}) - (4 x^{2}) - (- 9 x) - 1 \cdot 1$

Simplify.

Multiply $9$ by $- 1$ .

$7 x^{2} - 4 x - 3 - 9 x^{3} - (4 x^{2}) - (- 9 x) - 1 \cdot 1$

Multiply $4$ by $- 1$ .

$7 x^{2} - 4 x - 3 - 9 x^{3} - 4 x^{2} - (- 9 x) - 1 \cdot 1$

Multiply $- 9$ by $- 1$ .

$7 x^{2} - 4 x - 3 - 9 x^{3} - 4 x^{2} + 9 x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$7 x^{2} - 4 x - 3 - 9 x^{3} - 4 x^{2} + 9 x - 1$

Step 2

Simplify by adding terms.

Subtract $4 x^{2}$ from $7 x^{2}$ .

$3 x^{2} - 4 x - 3 - 9 x^{3} + 9 x - 1$

Add $- 4 x$ and $9 x$ .

$3 x^{2} + 5 x - 3 - 9 x^{3} - 1$

Simplify the expression.

Subtract $1$ from $- 3$ .

$3 x^{2} + 5 x - 9 x^{3} - 4$

Move $5 x$ .

$3 x^{2} - 9 x^{3} + 5 x - 4$

Reorder $3 x^{2}$ and $- 9 x^{3}$ .

$- 9 x^{3} + 3 x^{2} + 5 x - 4$