Basic Math Examples

$4 {(q - 1)}^{2}$

Step 1

Rewrite ${(q - 1)}^{2}$ as $(q - 1) (q - 1)$ .

$4 ((q - 1) (q - 1))$

Step 2

Expand $(q - 1) (q - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$4 (q (q - 1) - 1 (q - 1))$

Step 2.2

Apply the distributive property.

$4 (q \cdot q + q \cdot - 1 - 1 (q - 1))$

Step 2.3

Apply the distributive property.

$4 (q \cdot q + q \cdot - 1 - 1 q - 1 \cdot - 1)$

$4 (q \cdot q + q \cdot - 1 - 1 q - 1 \cdot - 1)$

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 $q$ by $q$ .

$4 (q^{2} + q \cdot - 1 - 1 q - 1 \cdot - 1)$

Step 3.1.2

Move $- 1$ to the left of $q$ .

$4 (q^{2} - 1 \cdot q - 1 q - 1 \cdot - 1)$

Step 3.1.3

Rewrite $- 1 q$ as $- q$ .

$4 (q^{2} - q - 1 q - 1 \cdot - 1)$

Step 3.1.4

Rewrite $- 1 q$ as $- q$ .

$4 (q^{2} - q - q - 1 \cdot - 1)$

Step 3.1.5

Multiply $- 1$ by $- 1$ .

$4 (q^{2} - q - q + 1)$

$4 (q^{2} - q - q + 1)$

Step 3.2

Subtract $q$ from $- q$ .

$4 (q^{2} - 2 q + 1)$

$4 (q^{2} - 2 q + 1)$

Step 4

Apply the distributive property.

$4 q^{2} + 4 (- 2 q) + 4 \cdot 1$

Step 5

Simplify.

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Step 5.1

Multiply $- 2$ by $4$ .

$4 q^{2} - 8 q + 4 \cdot 1$

Step 5.2

Multiply $4$ by $1$ .

$4 q^{2} - 8 q + 4$

$4 q^{2} - 8 q + 4$

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