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Examples

x^{2} + x + 1

$x^{2} + x + 1$ ,

x^{2} + 8 x + 1

$x^{2} + 8 x + 1$

Step 1

Subtract the second expression

x^{2} + 8 x + 1

$x^{2} + 8 x + 1$ from the first expression

x^{2} + x + 1

$x^{2} + x + 1$ .

x^{2} + x + 1 - (x^{2} + 8 x + 1)

$x^{2} + x + 1 - (x^{2} + 8 x + 1)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

x^{2} + x + 1 - x^{2} - (8 x) - 1 \cdot 1

$x^{2} + x + 1 - x^{2} - (8 x) - 1 \cdot 1$

Step 2.2

Simplify.

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Step 2.2.1

Multiply

8

$8$ by

- 1

$- 1$ .

x^{2} + x + 1 - x^{2} - 8 x - 1 \cdot 1

$x^{2} + x + 1 - x^{2} - 8 x - 1 \cdot 1$

Step 2.2.2

Multiply

- 1

$- 1$ by

1

$1$ .

x^{2} + x + 1 - x^{2} - 8 x - 1

$x^{2} + x + 1 - x^{2} - 8 x - 1$

x^{2} + x + 1 - x^{2} - 8 x - 1

$x^{2} + x + 1 - x^{2} - 8 x - 1$

x^{2} + x + 1 - x^{2} - 8 x - 1

$x^{2} + x + 1 - x^{2} - 8 x - 1$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in

x^{2} + x + 1 - x^{2} - 8 x - 1

$x^{2} + x + 1 - x^{2} - 8 x - 1$ .

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Step 3.1.1

Subtract

x^{2}

$x^{2}$ from

x^{2}

$x^{2}$ .

x + 1 + 0 - 8 x - 1

$x + 1 + 0 - 8 x - 1$

Step 3.1.2

Add

x + 1

$x + 1$ and

0

$0$ .

x + 1 - 8 x - 1

$x + 1 - 8 x - 1$

Step 3.1.3

Subtract

1

$1$ from

1

$1$ .

x - 8 x + 0

$x - 8 x + 0$

Step 3.1.4

Add

x - 8 x

$x - 8 x$ and

0

$0$ .

x - 8 x

$x - 8 x$

x - 8 x

$x - 8 x$

Step 3.2

Subtract

8 x

$8 x$ from

x

$x$ .

- 7 x

$- 7 x$

- 7 x

$- 7 x$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$