Basic Math Examples

$a^{2} - {(b + 1)}^{2}$

Step 1

Rewrite ${(b + 1)}^{2}$ as $(b + 1) (b + 1)$ .

$a^{2} - ((b + 1) (b + 1))$

Step 2

Expand $(b + 1) (b + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$a^{2} - (b (b + 1) + 1 (b + 1))$

Step 2.2

Apply the distributive property.

$a^{2} - (b \cdot b + b \cdot 1 + 1 (b + 1))$

Step 2.3

Apply the distributive property.

$a^{2} - (b \cdot b + b \cdot 1 + 1 b + 1 \cdot 1)$

$a^{2} - (b \cdot b + b \cdot 1 + 1 b + 1 \cdot 1)$

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 $b$ by $b$ .

$a^{2} - (b^{2} + b \cdot 1 + 1 b + 1 \cdot 1)$

Step 3.1.2

Multiply $b$ by $1$ .

$a^{2} - (b^{2} + b + 1 b + 1 \cdot 1)$

Step 3.1.3

Multiply $b$ by $1$ .

$a^{2} - (b^{2} + b + b + 1 \cdot 1)$

Step 3.1.4

Multiply $1$ by $1$ .

$a^{2} - (b^{2} + b + b + 1)$

$a^{2} - (b^{2} + b + b + 1)$

Step 3.2

Add $b$ and $b$ .

$a^{2} - (b^{2} + 2 b + 1)$

$a^{2} - (b^{2} + 2 b + 1)$

Step 4

Apply the distributive property.

$a^{2} - b^{2} - (2 b) - 1 \cdot 1$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $- 1$ .

$a^{2} - b^{2} - 2 b - 1 \cdot 1$

Step 5.2

Multiply $- 1$ by $1$ .

$a^{2} - b^{2} - 2 b - 1$

$a^{2} - b^{2} - 2 b - 1$

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