Solve (x + 2) ^ 2 + (x - 3) ^ 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

$$(x+2)^{2}+(x-3)^{2}$$

Expand

$2x^{2}-2x+13$

Solution Steps

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

$$x^{2}+4x+4+\left(x-3\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-3\right)^{2}$.

$$x^{2}+4x+4+x^{2}-6x+9$$

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

$$2x^{2}+4x+4-6x+9$$

Combine $4x$ and $-6x$ to get $-2x$.

$$2x^{2}-2x+4+9$$

Add $4$ and $9$ to get $13$.

$$2x^{2}-2x+13$$

Evaluate

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

Solution Steps

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

$$x^{2}+4x+4+\left(x-3\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-3\right)^{2}$.

$$x^{2}+4x+4+x^{2}-6x+9$$

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

$$2x^{2}+4x+4-6x+9$$

Combine $4x$ and $-6x$ to get $-2x$.

$$2x^{2}-2x+4+9$$

Add $4$ and $9$ to get $13$.

$$2x^{2}-2x+13$$