Solve ((x)/(2)+1)((x)/(2)-1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$( \frac{ x }{ 2 } +1)( \frac{ x }{ 2 } -1)$$

Evaluate

$\frac{x^{2}}{4}-1$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{2}{2}$.

$$\left(\frac{x}{2}+\frac{2}{2}\right)\left(\frac{x}{2}-1\right)$$

Since $\frac{x}{2}$ and $\frac{2}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{2}\left(\frac{x}{2}-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{2}{2}$.

$$\frac{x+2}{2}\left(\frac{x}{2}-\frac{2}{2}\right)$$

Since $\frac{x}{2}$ and $\frac{2}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2}{2}\times \frac{x-2}{2}$$

Multiply $\frac{x+2}{2}$ times $\frac{x-2}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x-2\right)}{2\times 2}$$

Multiply $2$ and $2$ to get $4$.

$$\frac{\left(x+2\right)\left(x-2\right)}{4}$$

Consider $\left(x+2\right)\left(x-2\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{x^{2}-2^{2}}{4}$$

Calculate $2$ to the power of $2$ and get $4$.

$$\frac{x^{2}-4}{4}$$

Expand

$\frac{x^{2}}{4}-1$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{2}{2}$.

$$\left(\frac{x}{2}+\frac{2}{2}\right)\left(\frac{x}{2}-1\right)$$

Since $\frac{x}{2}$ and $\frac{2}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{x+2}{2}\left(\frac{x}{2}-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{2}{2}$.

$$\frac{x+2}{2}\left(\frac{x}{2}-\frac{2}{2}\right)$$

Since $\frac{x}{2}$ and $\frac{2}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+2}{2}\times \frac{x-2}{2}$$

Multiply $\frac{x+2}{2}$ times $\frac{x-2}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x-2\right)}{2\times 2}$$

Multiply $2$ and $2$ to get $4$.

$$\frac{\left(x+2\right)\left(x-2\right)}{4}$$

Consider $\left(x+2\right)\left(x-2\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{x^{2}-2^{2}}{4}$$

Calculate $2$ to the power of $2$ and get $4$.

$$\frac{x^{2}-4}{4}$$