Simplify (4x^5-7x^3-9x^2+18)-(14x^5-8x^4+11x^2+x)

$(4 x^{5} - 7 x^{3} - 9 x^{2} + 18) - (14 x^{5} - 8 x^{4} + 11 x^{2} + x)$

Step 1

Simplify each term.

Apply the distributive property.

$4 x^{5} - 7 x^{3} - 9 x^{2} + 18 - (14 x^{5}) - (- 8 x^{4}) - (11 x^{2}) - x$

Simplify.

Multiply $14$ by $- 1$ .

$4 x^{5} - 7 x^{3} - 9 x^{2} + 18 - 14 x^{5} - (- 8 x^{4}) - (11 x^{2}) - x$

Multiply $- 8$ by $- 1$ .

$4 x^{5} - 7 x^{3} - 9 x^{2} + 18 - 14 x^{5} + 8 x^{4} - (11 x^{2}) - x$

Multiply $11$ by $- 1$ .

$4 x^{5} - 7 x^{3} - 9 x^{2} + 18 - 14 x^{5} + 8 x^{4} - 11 x^{2} - x$

Step 2

Simplify by adding terms.

Subtract $14 x^{5}$ from $4 x^{5}$ .

$- 10 x^{5} - 7 x^{3} - 9 x^{2} + 18 + 8 x^{4} - 11 x^{2} - x$

Subtract $11 x^{2}$ from $- 9 x^{2}$ .

$- 10 x^{5} - 7 x^{3} - 20 x^{2} + 18 + 8 x^{4} - x$

Reorder.

Move $18$ .

$- 10 x^{5} - 7 x^{3} - 20 x^{2} + 8 x^{4} - x + 18$

Move $- 20 x^{2}$ .

$- 10 x^{5} - 7 x^{3} + 8 x^{4} - 20 x^{2} - x + 18$

Move $- 7 x^{3}$ .

$- 10 x^{5} + 8 x^{4} - 7 x^{3} - 20 x^{2} - x + 18$