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Pre-Algebra Examples

x^{3} + x^{2} + 1

$x^{3} + x^{2} + 1$ ,

x^{2} + 7 x + 1

$x^{2} + 7 x + 1$

Step 1

Subtract the second expression

x^{2} + 7 x + 1

$x^{2} + 7 x + 1$ from the first expression

x^{3} + x^{2} + 1

$x^{3} + x^{2} + 1$ .

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

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

x^{3} + x^{2} + 1 - x^{2} - (7 x) - 1 \cdot 1

$x^{3} + x^{2} + 1 - x^{2} - (7 x) - 1 \cdot 1$

Step 2.2

Simplify.

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Step 2.2.1

Multiply

7

$7$ by

- 1

$- 1$ .

x^{3} + x^{2} + 1 - x^{2} - 7 x - 1 \cdot 1

$x^{3} + x^{2} + 1 - x^{2} - 7 x - 1 \cdot 1$

Step 2.2.2

Multiply

- 1

$- 1$ by

1

$1$ .

x^{3} + x^{2} + 1 - x^{2} - 7 x - 1

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

x^{3} + x^{2} + 1 - x^{2} - 7 x - 1

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

x^{3} + x^{2} + 1 - x^{2} - 7 x - 1

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

Step 3

Combine the opposite terms in

x^{3} + x^{2} + 1 - x^{2} - 7 x - 1

$x^{3} + x^{2} + 1 - x^{2} - 7 x - 1$ .

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Step 3.1

Subtract

x^{2}

$x^{2}$ from

x^{2}

$x^{2}$ .

x^{3} + 0 + 1 - 7 x - 1

$x^{3} + 0 + 1 - 7 x - 1$

Step 3.2

Add

x^{3}

$x^{3}$ and

0

$0$ .

x^{3} + 1 - 7 x - 1

$x^{3} + 1 - 7 x - 1$

Step 3.3

Subtract

1

$1$ from

1

$1$ .

x^{3} - 7 x + 0

$x^{3} - 7 x + 0$

Step 3.4

Add

x^{3} - 7 x

$x^{3} - 7 x$ and

0

$0$ .

x^{3} - 7 x

$x^{3} - 7 x$

x^{3} - 7 x

$x^{3} - 7 x$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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