Solve (a + b) ^ 2 - (a - b) ^ 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

$$(a+b)^{2}-(a-b)^{2}$$

Evaluate

$4ab$

Solution Steps

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

$$a^{2}+2ab+b^{2}-\left(a-b\right)^{2}$$

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-b\right)^{2}$.

$$a^{2}+2ab+b^{2}-\left(a^{2}-2ab+b^{2}\right)$$

To find the opposite of $a^{2}-2ab+b^{2}$, find the opposite of each term.

$$a^{2}+2ab+b^{2}-a^{2}+2ab-b^{2}$$

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

$$2ab+b^{2}+2ab-b^{2}$$

Combine $2ab$ and $2ab$ to get $4ab$.

$$4ab+b^{2}-b^{2}$$

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

$$4ab$$

Expand

$4ab$

Solution Steps

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

$$a^{2}+2ab+b^{2}-\left(a-b\right)^{2}$$

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a-b\right)^{2}$.

$$a^{2}+2ab+b^{2}-\left(a^{2}-2ab+b^{2}\right)$$

To find the opposite of $a^{2}-2ab+b^{2}$, find the opposite of each term.

$$a^{2}+2ab+b^{2}-a^{2}+2ab-b^{2}$$

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

$$2ab+b^{2}+2ab-b^{2}$$

Combine $2ab$ and $2ab$ to get $4ab$.

$$4ab+b^{2}-b^{2}$$

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

$$4ab$$