Algebra Examples

$(6 x - 7 x^{2} + 7) - (5 x^{2} + 2 x - 2 x^{3} - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$6 x - 7 x^{2} + 7 - (5 x^{2}) - (2 x) - (- 2 x^{3}) - - 1$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$6 x - 7 x^{2} + 7 - 5 x^{2} - (2 x) - (- 2 x^{3}) - - 1$

Step 1.2.2

Multiply $2$ by $- 1$ .

$6 x - 7 x^{2} + 7 - 5 x^{2} - 2 x - (- 2 x^{3}) - - 1$

Step 1.2.3

Multiply $- 2$ by $- 1$ .

$6 x - 7 x^{2} + 7 - 5 x^{2} - 2 x + 2 x^{3} - - 1$

Step 1.2.4

Multiply $- 1$ by $- 1$ .

$6 x - 7 x^{2} + 7 - 5 x^{2} - 2 x + 2 x^{3} + 1$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x$ from $6 x$ .

$- 7 x^{2} + 7 - 5 x^{2} + 4 x + 2 x^{3} + 1$

Step 2.2

Subtract $5 x^{2}$ from $- 7 x^{2}$ .

$- 12 x^{2} + 7 + 4 x + 2 x^{3} + 1$

Step 2.3

Simplify the expression.

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Step 2.3.1

Add $7$ and $1$ .

$- 12 x^{2} + 4 x + 2 x^{3} + 8$

Step 2.3.2

Move $4 x$ .

$- 12 x^{2} + 2 x^{3} + 4 x + 8$

Step 2.3.3

Reorder $- 12 x^{2}$ and $2 x^{3}$ .

$2 x^{3} - 12 x^{2} + 4 x + 8$