Solve (x + 7) ^ 2 - (x - 5) ^ 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

$$(x+7)^{2}-(x-5)^{2}$$

Evaluate

$24\left(x+1\right)$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+7\right)^{2}$.

$$x^{2}+14x+49-\left(x-5\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-5\right)^{2}$.

$$x^{2}+14x+49-\left(x^{2}-10x+25\right)$$

To find the opposite of $x^{2}-10x+25$, find the opposite of each term.

$$x^{2}+14x+49-x^{2}+10x-25$$

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

$$14x+49+10x-25$$

Combine $14x$ and $10x$ to get $24x$.

$$24x+49-25$$

Subtract $25$ from $49$ to get $24$.

$$24x+24$$

Expand

$24x+24$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+7\right)^{2}$.

$$x^{2}+14x+49-\left(x-5\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-5\right)^{2}$.

$$x^{2}+14x+49-\left(x^{2}-10x+25\right)$$

To find the opposite of $x^{2}-10x+25$, find the opposite of each term.

$$x^{2}+14x+49-x^{2}+10x-25$$

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

$$14x+49+10x-25$$

Combine $14x$ and $10x$ to get $24x$.

$$24x+49-25$$

Subtract $25$ from $49$ to get $24$.

$$24x+24$$