Pre-Algebra Examples

$(7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6) - (2 x^{4} + 3 x^{3} - x^{2} + x - 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - (2 x^{4}) - (3 x^{3}) - - x^{2} - x - - 4$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

$7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - 2 x^{4} - (3 x^{3}) - - x^{2} - x - - 4$

Step 1.2.2

Multiply $3$ by $- 1$ .

$7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - 2 x^{4} - 3 x^{3} - - x^{2} - x - - 4$

Step 1.2.3

Multiply $- - x^{2}$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - 2 x^{4} - 3 x^{3} + 1 x^{2} - x - - 4$

Step 1.2.3.2

Multiply $x^{2}$ by $1$ .

$7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - 2 x^{4} - 3 x^{3} + x^{2} - x - - 4$

Step 1.2.4

Multiply $- 1$ by $- 4$ .

$7 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - 2 x^{4} - 3 x^{3} + x^{2} - x + 4$

Step 2

Simplify by adding terms.

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Step 2.1

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

$5 x^{4} - 9 x^{3} - 4 x^{2} + 5 x + 6 - 3 x^{3} + x^{2} - x + 4$

Step 2.2

Subtract $3 x^{3}$ from $- 9 x^{3}$ .

$5 x^{4} - 12 x^{3} - 4 x^{2} + 5 x + 6 + x^{2} - x + 4$

Step 2.3

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

$5 x^{4} - 12 x^{3} - 3 x^{2} + 5 x + 6 - x + 4$

Step 2.4

Subtract $x$ from $5 x$ .

$5 x^{4} - 12 x^{3} - 3 x^{2} + 4 x + 6 + 4$

Step 2.5

Add $6$ and $4$ .

$5 x^{4} - 12 x^{3} - 3 x^{2} + 4 x + 10$