Solve ((2)/(5)x-(3)/(4)y)((2)/(5)x+(1)/(4)y) | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$( \frac{ 2 }{ 5 } x- \frac{ 3 }{ 4 } y)( \frac{ 2 }{ 5 } x+ \frac{ 1 }{ 4 } y)$$

Evaluate

$-\frac{xy}{5}+\frac{4x^{2}}{25}-\frac{3y^{2}}{16}$

Solution Steps

Apply the distributive property by multiplying each term of $\frac{2}{5}x-\frac{3}{4}y$ by each term of $\frac{2}{5}x+\frac{1}{4}y$.

$$\frac{2}{5}x\times \frac{2}{5}x+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y\times \frac{1}{4}y$$

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

$$\frac{2}{5}x^{2}\times \frac{2}{5}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y\times \frac{1}{4}y$$

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

$$\frac{2}{5}x^{2}\times \frac{2}{5}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

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

$$\frac{2\times 2}{5\times 5}x^{2}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Do the multiplications in the fraction $\frac{2\times 2}{5\times 5}$.

$$\frac{4}{25}x^{2}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Multiply $\frac{2}{5}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{25}x^{2}+\frac{2\times 1}{5\times 4}xy-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Do the multiplications in the fraction $\frac{2\times 1}{5\times 4}$.

$$\frac{4}{25}x^{2}+\frac{2}{20}xy-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Reduce the fraction $\frac{2}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Multiply $-\frac{3}{4}$ times $\frac{2}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy+\frac{-3\times 2}{4\times 5}yx-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Do the multiplications in the fraction $\frac{-3\times 2}{4\times 5}$.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy+\frac{-6}{20}yx-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Reduce the fraction $\frac{-6}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy-\frac{3}{10}yx-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Combine $\frac{1}{10}xy$ and $-\frac{3}{10}yx$ to get $-\frac{1}{5}xy$.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Multiply $-\frac{3}{4}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy+\frac{-3}{4\times 4}y^{2}$$

Do the multiplications in the fraction $\frac{-3}{4\times 4}$.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy+\frac{-3}{16}y^{2}$$

Fraction $\frac{-3}{16}$ can be rewritten as $-\frac{3}{16}$ by extracting the negative sign.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy-\frac{3}{16}y^{2}$$

Expand

$-\frac{xy}{5}+\frac{4x^{2}}{25}-\frac{3y^{2}}{16}$

Solution Steps

Apply the distributive property by multiplying each term of $\frac{2}{5}x-\frac{3}{4}y$ by each term of $\frac{2}{5}x+\frac{1}{4}y$.

$$\frac{2}{5}x\times \frac{2}{5}x+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y\times \frac{1}{4}y$$

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

$$\frac{2}{5}x^{2}\times \frac{2}{5}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y\times \frac{1}{4}y$$

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

$$\frac{2}{5}x^{2}\times \frac{2}{5}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

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

$$\frac{2\times 2}{5\times 5}x^{2}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Do the multiplications in the fraction $\frac{2\times 2}{5\times 5}$.

$$\frac{4}{25}x^{2}+\frac{2}{5}x\times \frac{1}{4}y-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Multiply $\frac{2}{5}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{25}x^{2}+\frac{2\times 1}{5\times 4}xy-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Do the multiplications in the fraction $\frac{2\times 1}{5\times 4}$.

$$\frac{4}{25}x^{2}+\frac{2}{20}xy-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Reduce the fraction $\frac{2}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy-\frac{3}{4}y\times \frac{2}{5}x-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Multiply $-\frac{3}{4}$ times $\frac{2}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy+\frac{-3\times 2}{4\times 5}yx-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Do the multiplications in the fraction $\frac{-3\times 2}{4\times 5}$.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy+\frac{-6}{20}yx-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Reduce the fraction $\frac{-6}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{4}{25}x^{2}+\frac{1}{10}xy-\frac{3}{10}yx-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Combine $\frac{1}{10}xy$ and $-\frac{3}{10}yx$ to get $-\frac{1}{5}xy$.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy-\frac{3}{4}y^{2}\times \frac{1}{4}$$

Multiply $-\frac{3}{4}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy+\frac{-3}{4\times 4}y^{2}$$

Do the multiplications in the fraction $\frac{-3}{4\times 4}$.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy+\frac{-3}{16}y^{2}$$

Fraction $\frac{-3}{16}$ can be rewritten as $-\frac{3}{16}$ by extracting the negative sign.

$$\frac{4}{25}x^{2}-\frac{1}{5}xy-\frac{3}{16}y^{2}$$