Pre-Algebra Examples

(y^{2} - 4 y + 9) - (3 y^{2} - 6 y - 9)

$(y^{2} - 4 y + 9) - (3 y^{2} - 6 y - 9)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

y^{2} - 4 y + 9 - (3 y^{2}) - (- 6 y) - - 9

$y^{2} - 4 y + 9 - (3 y^{2}) - (- 6 y) - - 9$

Step 1.2

Simplify.

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Step 1.2.1

Multiply

3

$3$ by

- 1

$- 1$ .

y^{2} - 4 y + 9 - 3 y^{2} - (- 6 y) - - 9

$y^{2} - 4 y + 9 - 3 y^{2} - (- 6 y) - - 9$

Step 1.2.2

Multiply

- 6

$- 6$ by

- 1

$- 1$ .

y^{2} - 4 y + 9 - 3 y^{2} + 6 y - - 9

$y^{2} - 4 y + 9 - 3 y^{2} + 6 y - - 9$

Step 1.2.3

Multiply

- 1

$- 1$ by

- 9

$- 9$ .

y^{2} - 4 y + 9 - 3 y^{2} + 6 y + 9

$y^{2} - 4 y + 9 - 3 y^{2} + 6 y + 9$

y^{2} - 4 y + 9 - 3 y^{2} + 6 y + 9

$y^{2} - 4 y + 9 - 3 y^{2} + 6 y + 9$

y^{2} - 4 y + 9 - 3 y^{2} + 6 y + 9

$y^{2} - 4 y + 9 - 3 y^{2} + 6 y + 9$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract

3 y^{2}

$3 y^{2}$ from

y^{2}

$y^{2}$ .

- 2 y^{2} - 4 y + 9 + 6 y + 9

$- 2 y^{2} - 4 y + 9 + 6 y + 9$

Step 2.2

Add

- 4 y

$- 4 y$ and

6 y

$6 y$ .

- 2 y^{2} + 2 y + 9 + 9

$- 2 y^{2} + 2 y + 9 + 9$

Step 2.3

Add

9

$9$ and

9

$9$ .

- 2 y^{2} + 2 y + 18

$- 2 y^{2} + 2 y + 18$

- 2 y^{2} + 2 y + 18

$- 2 y^{2} + 2 y + 18$

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

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