Algebra Examples

$(x^{4} - 3 x^{3} + 5 x^{2} + x - 4) - (x^{3} - 4 x^{2} - 11 x + 10)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$x^{4} - 3 x^{3} + 5 x^{2} + x - 4 - x^{3} - (- 4 x^{2}) - (- 11 x) - 1 \cdot 10$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 4$ by $- 1$ .

$x^{4} - 3 x^{3} + 5 x^{2} + x - 4 - x^{3} + 4 x^{2} - (- 11 x) - 1 \cdot 10$

Step 2.2.2

Multiply $- 11$ by $- 1$ .

$x^{4} - 3 x^{3} + 5 x^{2} + x - 4 - x^{3} + 4 x^{2} + 11 x - 1 \cdot 10$

Step 2.2.3

Multiply $- 1$ by $10$ .

$x^{4} - 3 x^{3} + 5 x^{2} + x - 4 - x^{3} + 4 x^{2} + 11 x - 10$

Step 3

Simplify by adding terms.

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Step 3.1

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

$x^{4} - 4 x^{3} + 5 x^{2} + x - 4 + 4 x^{2} + 11 x - 10$

Step 3.2

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

$x^{4} - 4 x^{3} + 9 x^{2} + x - 4 + 11 x - 10$

Step 3.3

Add $x$ and $11 x$ .

$x^{4} - 4 x^{3} + 9 x^{2} + 12 x - 4 - 10$

Step 3.4

Subtract $10$ from $- 4$ .

$x^{4} - 4 x^{3} + 9 x^{2} + 12 x - 14$