Solve of (a/(2b) + (3b)/4)(a/(2b) - (3b)/4) ct 2 | 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

$$( \frac { a } { 2 b } + \frac { 3 b } { 4 } ) ( \frac { a } { 2 b } - \frac { 3 b } { 4 } )$$

Evaluate

$-\frac{9b^{2}}{16}+\frac{\left(\frac{a}{b}\right)^{2}}{4}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2b$ and $4$ is $4b$. Multiply $\frac{a}{2b}$ times $\frac{2}{2}$. Multiply $\frac{3b}{4}$ times $\frac{b}{b}$.

$$\left(\frac{2a}{4b}+\frac{3bb}{4b}\right)\left(\frac{a}{2b}-\frac{3b}{4}\right)$$

Since $\frac{2a}{4b}$ and $\frac{3bb}{4b}$ have the same denominator, add them by adding their numerators.

$$\frac{2a+3bb}{4b}\left(\frac{a}{2b}-\frac{3b}{4}\right)$$

Do the multiplications in $2a+3bb$.

$$\frac{2a+3b^{2}}{4b}\left(\frac{a}{2b}-\frac{3b}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2b$ and $4$ is $4b$. Multiply $\frac{a}{2b}$ times $\frac{2}{2}$. Multiply $\frac{3b}{4}$ times $\frac{b}{b}$.

$$\frac{2a+3b^{2}}{4b}\left(\frac{2a}{4b}-\frac{3bb}{4b}\right)$$

Since $\frac{2a}{4b}$ and $\frac{3bb}{4b}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2a+3b^{2}}{4b}\times \frac{2a-3bb}{4b}$$

Do the multiplications in $2a-3bb$.

$$\frac{2a+3b^{2}}{4b}\times \frac{2a-3b^{2}}{4b}$$

Multiply $\frac{2a+3b^{2}}{4b}$ times $\frac{2a-3b^{2}}{4b}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)}{4b\times 4b}$$

Multiply $b$ and $b$ to get $b^{2}$.

$$\frac{\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)}{4b^{2}\times 4}$$

Multiply $4$ and $4$ to get $16$.

$$\frac{\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)}{16b^{2}}$$

Consider $\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{\left(2a\right)^{2}-\left(3b^{2}\right)^{2}}{16b^{2}}$$

Expand $\left(2a\right)^{2}$.

$$\frac{2^{2}a^{2}-\left(3b^{2}\right)^{2}}{16b^{2}}$$

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

$$\frac{4a^{2}-\left(3b^{2}\right)^{2}}{16b^{2}}$$

Expand $\left(3b^{2}\right)^{2}$.

$$\frac{4a^{2}-3^{2}\left(b^{2}\right)^{2}}{16b^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$\frac{4a^{2}-3^{2}b^{4}}{16b^{2}}$$

Calculate $3$ to the power of $2$ and get $9$.

$$\frac{4a^{2}-9b^{4}}{16b^{2}}$$

Expand

$-\frac{9b^{2}}{16}+\frac{\left(\frac{a}{b}\right)^{2}}{4}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2b$ and $4$ is $4b$. Multiply $\frac{a}{2b}$ times $\frac{2}{2}$. Multiply $\frac{3b}{4}$ times $\frac{b}{b}$.

$$\left(\frac{2a}{4b}+\frac{3bb}{4b}\right)\left(\frac{a}{2b}-\frac{3b}{4}\right)$$

Since $\frac{2a}{4b}$ and $\frac{3bb}{4b}$ have the same denominator, add them by adding their numerators.

$$\frac{2a+3bb}{4b}\left(\frac{a}{2b}-\frac{3b}{4}\right)$$

Do the multiplications in $2a+3bb$.

$$\frac{2a+3b^{2}}{4b}\left(\frac{a}{2b}-\frac{3b}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2b$ and $4$ is $4b$. Multiply $\frac{a}{2b}$ times $\frac{2}{2}$. Multiply $\frac{3b}{4}$ times $\frac{b}{b}$.

$$\frac{2a+3b^{2}}{4b}\left(\frac{2a}{4b}-\frac{3bb}{4b}\right)$$

Since $\frac{2a}{4b}$ and $\frac{3bb}{4b}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{2a+3b^{2}}{4b}\times \frac{2a-3bb}{4b}$$

Do the multiplications in $2a-3bb$.

$$\frac{2a+3b^{2}}{4b}\times \frac{2a-3b^{2}}{4b}$$

Multiply $\frac{2a+3b^{2}}{4b}$ times $\frac{2a-3b^{2}}{4b}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)}{4b\times 4b}$$

Multiply $b$ and $b$ to get $b^{2}$.

$$\frac{\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)}{4b^{2}\times 4}$$

Multiply $4$ and $4$ to get $16$.

$$\frac{\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)}{16b^{2}}$$

Consider $\left(2a+3b^{2}\right)\left(2a-3b^{2}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

$$\frac{\left(2a\right)^{2}-\left(3b^{2}\right)^{2}}{16b^{2}}$$

Expand $\left(2a\right)^{2}$.

$$\frac{2^{2}a^{2}-\left(3b^{2}\right)^{2}}{16b^{2}}$$

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

$$\frac{4a^{2}-\left(3b^{2}\right)^{2}}{16b^{2}}$$

Expand $\left(3b^{2}\right)^{2}$.

$$\frac{4a^{2}-3^{2}\left(b^{2}\right)^{2}}{16b^{2}}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$\frac{4a^{2}-3^{2}b^{4}}{16b^{2}}$$

Calculate $3$ to the power of $2$ and get $9$.

$$\frac{4a^{2}-9b^{4}}{16b^{2}}$$