Algebra Examples

$3 x^{4} + 2 x^{3} - 5 x^{2} + 4 x^{2} + 6 x - 2 x - 3 x^{4} + 7 x^{5} - 3 x^{3}$

Step 1

Combine the opposite terms in $3 x^{4} + 2 x^{3} - 5 x^{2} + 4 x^{2} + 6 x - 2 x - 3 x^{4} + 7 x^{5} - 3 x^{3}$ .

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Step 1.1

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

$2 x^{3} - 5 x^{2} + 4 x^{2} + 6 x - 2 x + 0 + 7 x^{5} - 3 x^{3}$

Step 1.2

Add $2 x^{3} - 5 x^{2} + 4 x^{2} + 6 x - 2 x$ and $0$ .

$2 x^{3} - 5 x^{2} + 4 x^{2} + 6 x - 2 x + 7 x^{5} - 3 x^{3}$

Step 2

Subtract $3 x^{3}$ from $2 x^{3}$ .

$- x^{3} - 5 x^{2} + 4 x^{2} + 6 x - 2 x + 7 x^{5}$

Step 3

Add $- 5 x^{2}$ and $4 x^{2}$ .

$- x^{3} - x^{2} + 6 x - 2 x + 7 x^{5}$

Step 4

Subtract $2 x$ from $6 x$ .

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

Step 5

Simplify the expression.

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Step 5.1

Move $4 x$ .

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

Step 5.2

Move $- x^{2}$ .

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

Step 5.3

Reorder $- x^{3}$ and $7 x^{5}$ .

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