Solve (x - 1) ^ 2 - (x + 4) ^ 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

$$(x-1)^{2}-(x+4)^{2}$$

Evaluate

$-10x-15$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-1\right)^{2}$.

$$x^{2}-2x+1-\left(x+4\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+4\right)^{2}$.

$$x^{2}-2x+1-\left(x^{2}+8x+16\right)$$

To find the opposite of $x^{2}+8x+16$, find the opposite of each term.

$$x^{2}-2x+1-x^{2}-8x-16$$

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

$$-2x+1-8x-16$$

Combine $-2x$ and $-8x$ to get $-10x$.

$$-10x+1-16$$

Subtract $16$ from $1$ to get $-15$.

$$-10x-15$$

Expand

$-10x-15$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-1\right)^{2}$.

$$x^{2}-2x+1-\left(x+4\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+4\right)^{2}$.

$$x^{2}-2x+1-\left(x^{2}+8x+16\right)$$

To find the opposite of $x^{2}+8x+16$, find the opposite of each term.

$$x^{2}-2x+1-x^{2}-8x-16$$

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

$$-2x+1-8x-16$$

Combine $-2x$ and $-8x$ to get $-10x$.

$$-10x+1-16$$

Subtract $16$ from $1$ to get $-15$.

$$-10x-15$$