Algebra Examples

$v ({(x - 3)}^{2})$

Step 1

Rewrite ${(x - 3)}^{2}$ as $(x - 3) (x - 3)$ .

$v ((x - 3) (x - 3))$

Step 2

Expand $(x - 3) (x - 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$v (x (x - 3) - 3 (x - 3))$

Step 2.2

Apply the distributive property.

$v (x \cdot x + x \cdot - 3 - 3 (x - 3))$

Step 2.3

Apply the distributive property.

$v (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

$v (x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Move $- 3$ to the left of $x$ .

$v (x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3)$

Step 3.1.3

Multiply $- 3$ by $- 3$ .

$v (x^{2} - 3 x - 3 x + 9)$

$v (x^{2} - 3 x - 3 x + 9)$

Step 3.2

Subtract $3 x$ from $- 3 x$ .

$v (x^{2} - 6 x + 9)$

$v (x^{2} - 6 x + 9)$

Step 4

Apply the distributive property.

$v x^{2} + v (- 6 x) + v \cdot 9$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$v x^{2} - 6 v x + v \cdot 9$

Step 5.2

Move $9$ to the left of $v$ .

$v x^{2} - 6 v x + 9 \cdot v$

$v x^{2} - 6 v x + 9 v$

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