Solve । সরল কর : () (x + y) ^ 2 + 2(x + y)(x - y) + (x - y) ^ 2 | 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

$$( x + y ) ^ { 2 } + 2 ( x + y ) ( x - y ) + ( x - y ) ^ { 2 }$$

Evaluate

$4x^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+y\right)^{2}$.

$$x^{2}+2xy+y^{2}+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

Use the distributive property to multiply $2$ by $x+y$.

$$x^{2}+2xy+y^{2}+\left(2x+2y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

Use the distributive property to multiply $2x+2y$ by $x-y$ and combine like terms.

$$x^{2}+2xy+y^{2}+2x^{2}-2y^{2}+\left(x-y\right)^{2}$$

Combine $x^{2}$ and $2x^{2}$ to get $3x^{2}$.

$$3x^{2}+2xy+y^{2}-2y^{2}+\left(x-y\right)^{2}$$

Combine $y^{2}$ and $-2y^{2}$ to get $-y^{2}$.

$$3x^{2}+2xy-y^{2}+\left(x-y\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-y\right)^{2}$.

$$3x^{2}+2xy-y^{2}+x^{2}-2xy+y^{2}$$

Combine $3x^{2}$ and $x^{2}$ to get $4x^{2}$.

$$4x^{2}+2xy-y^{2}-2xy+y^{2}$$

Combine $2xy$ and $-2xy$ to get $0$.

$$4x^{2}-y^{2}+y^{2}$$

Combine $-y^{2}$ and $y^{2}$ to get $0$.

$$4x^{2}$$

Expand

$4x^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+y\right)^{2}$.

$$x^{2}+2xy+y^{2}+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

Use the distributive property to multiply $2$ by $x+y$.

$$x^{2}+2xy+y^{2}+\left(2x+2y\right)\left(x-y\right)+\left(x-y\right)^{2}$$

Use the distributive property to multiply $2x+2y$ by $x-y$ and combine like terms.

$$x^{2}+2xy+y^{2}+2x^{2}-2y^{2}+\left(x-y\right)^{2}$$

Combine $x^{2}$ and $2x^{2}$ to get $3x^{2}$.

$$3x^{2}+2xy+y^{2}-2y^{2}+\left(x-y\right)^{2}$$

Combine $y^{2}$ and $-2y^{2}$ to get $-y^{2}$.

$$3x^{2}+2xy-y^{2}+\left(x-y\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-y\right)^{2}$.

$$3x^{2}+2xy-y^{2}+x^{2}-2xy+y^{2}$$

Combine $3x^{2}$ and $x^{2}$ to get $4x^{2}$.

$$4x^{2}+2xy-y^{2}-2xy+y^{2}$$

Combine $2xy$ and $-2xy$ to get $0$.

$$4x^{2}-y^{2}+y^{2}$$

Combine $-y^{2}$ and $y^{2}$ to get $0$.

$$4x^{2}$$