Solve គ . (4/5 * x - y/2)(4/5 * x + y/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

$$( \frac { 4 } { 5 } x - \frac { y } { 2 } ) ( \frac { 4 } { 5 } x + \frac { y } { 2 } )$$

Evaluate

$\frac{16x^{2}}{25}-\frac{y^{2}}{4}$

Short Solution Steps

Apply the distributive property by multiplying each term of $\frac{4}{5}x-\frac{y}{2}$ by each term of $\frac{4}{5}x+\frac{y}{2}$.

$$\frac{4}{5}x\times \frac{4}{5}x+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

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

$$\frac{4}{5}x^{2}\times \frac{4}{5}+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Multiply $\frac{4}{5}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 4}{5\times 5}x^{2}+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Do the multiplications in the fraction $\frac{4\times 4}{5\times 5}$.

$$\frac{16}{25}x^{2}+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Multiply $\frac{4}{5}$ times $\frac{y}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{25}x^{2}+\frac{4y}{5\times 2}x+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Multiply $-\frac{y}{2}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-y\times 4}{2\times 5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-2y}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Express $\frac{-2y}{5}x$ as a single fraction.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-2yx}{5}+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

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

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-2yx}{5}+\frac{-yy}{2\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5$ and $2\times 2$ is $20$. Multiply $\frac{-2yx}{5}$ times $\frac{4}{4}$. Multiply $\frac{-yy}{2\times 2}$ times $\frac{5}{5}$.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{4\left(-1\right)\times 2yx}{20}+\frac{5\left(-1\right)yy}{20}$$

Since $\frac{4\left(-1\right)\times 2yx}{20}$ and $\frac{5\left(-1\right)yy}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{4\left(-1\right)\times 2yx+5\left(-1\right)yy}{20}$$

Do the multiplications in $4\left(-1\right)\times 2yx+5\left(-1\right)yy$.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-8yx-5y^{2}}{20}$$

Express $\frac{2y}{5}x$ as a single fraction.

$$\frac{16}{25}x^{2}+\frac{2yx}{5}+\frac{-8yx-5y^{2}}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5$ and $20$ is $20$. Multiply $\frac{2yx}{5}$ times $\frac{4}{4}$.

$$\frac{16}{25}x^{2}+\frac{4\times 2yx}{20}+\frac{-8yx-5y^{2}}{20}$$

Since $\frac{4\times 2yx}{20}$ and $\frac{-8yx-5y^{2}}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{16}{25}x^{2}+\frac{4\times 2yx-8yx-5y^{2}}{20}$$

Do the multiplications in $4\times 2yx-8yx-5y^{2}$.

$$\frac{16}{25}x^{2}+\frac{8yx-8yx-5y^{2}}{20}$$

Combine like terms in $8yx-8yx-5y^{2}$.

$$\frac{16}{25}x^{2}+\frac{-5y^{2}}{20}$$

Divide $-5y^{2}$ by $20$ to get $-\frac{1}{4}y^{2}$.

$$\frac{16}{25}x^{2}-\frac{1}{4}y^{2}$$

Expand

$\frac{16x^{2}}{25}-\frac{y^{2}}{4}$

Short Solution Steps

Apply the distributive property by multiplying each term of $\frac{4}{5}x-\frac{y}{2}$ by each term of $\frac{4}{5}x+\frac{y}{2}$.

$$\frac{4}{5}x\times \frac{4}{5}x+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

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

$$\frac{4}{5}x^{2}\times \frac{4}{5}+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Multiply $\frac{4}{5}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 4}{5\times 5}x^{2}+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Do the multiplications in the fraction $\frac{4\times 4}{5\times 5}$.

$$\frac{16}{25}x^{2}+\frac{4}{5}x\times \frac{y}{2}+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Multiply $\frac{4}{5}$ times $\frac{y}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{25}x^{2}+\frac{4y}{5\times 2}x+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\left(-\frac{y}{2}\right)\times \frac{4}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Multiply $-\frac{y}{2}$ times $\frac{4}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-y\times 4}{2\times 5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-2y}{5}x+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

Express $\frac{-2y}{5}x$ as a single fraction.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-2yx}{5}+\left(-\frac{y}{2}\right)\times \frac{y}{2}$$

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

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-2yx}{5}+\frac{-yy}{2\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5$ and $2\times 2$ is $20$. Multiply $\frac{-2yx}{5}$ times $\frac{4}{4}$. Multiply $\frac{-yy}{2\times 2}$ times $\frac{5}{5}$.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{4\left(-1\right)\times 2yx}{20}+\frac{5\left(-1\right)yy}{20}$$

Since $\frac{4\left(-1\right)\times 2yx}{20}$ and $\frac{5\left(-1\right)yy}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{4\left(-1\right)\times 2yx+5\left(-1\right)yy}{20}$$

Do the multiplications in $4\left(-1\right)\times 2yx+5\left(-1\right)yy$.

$$\frac{16}{25}x^{2}+\frac{2y}{5}x+\frac{-8yx-5y^{2}}{20}$$

Express $\frac{2y}{5}x$ as a single fraction.

$$\frac{16}{25}x^{2}+\frac{2yx}{5}+\frac{-8yx-5y^{2}}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5$ and $20$ is $20$. Multiply $\frac{2yx}{5}$ times $\frac{4}{4}$.

$$\frac{16}{25}x^{2}+\frac{4\times 2yx}{20}+\frac{-8yx-5y^{2}}{20}$$

Since $\frac{4\times 2yx}{20}$ and $\frac{-8yx-5y^{2}}{20}$ have the same denominator, add them by adding their numerators.

$$\frac{16}{25}x^{2}+\frac{4\times 2yx-8yx-5y^{2}}{20}$$

Do the multiplications in $4\times 2yx-8yx-5y^{2}$.

$$\frac{16}{25}x^{2}+\frac{8yx-8yx-5y^{2}}{20}$$

Combine like terms in $8yx-8yx-5y^{2}$.

$$\frac{16}{25}x^{2}+\frac{-5y^{2}}{20}$$

Divide $-5y^{2}$ by $20$ to get $-\frac{1}{4}y^{2}$.

$$\frac{16}{25}x^{2}-\frac{1}{4}y^{2}$$