Solve (x - 6)(5x - 1)(x - 6) | 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

$$(x-6)(5x-1)(x-6)$$

Evaluate

$\left(5x-1\right)\left(x-6\right)^{2}$

Solution Steps

Multiply $x-6$ and $x-6$ to get $\left(x-6\right)^{2}$.

$$\left(x-6\right)^{2}\left(5x-1\right)$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-6\right)^{2}$.

$$\left(x^{2}-12x+36\right)\left(5x-1\right)$$

Apply the distributive property by multiplying each term of $x^{2}-12x+36$ by each term of $5x-1$.

$$5x^{3}-x^{2}-60x^{2}+12x+180x-36$$

Combine $-x^{2}$ and $-60x^{2}$ to get $-61x^{2}$.

$$5x^{3}-61x^{2}+12x+180x-36$$

Combine $12x$ and $180x$ to get $192x$.

$$5x^{3}-61x^{2}+192x-36$$

Expand

$5x^{3}-61x^{2}+192x-36$

Solution Steps

Multiply $x-6$ and $x-6$ to get $\left(x-6\right)^{2}$.

$$\left(x-6\right)^{2}\left(5x-1\right)$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-6\right)^{2}$.

$$\left(x^{2}-12x+36\right)\left(5x-1\right)$$

Apply the distributive property by multiplying each term of $x^{2}-12x+36$ by each term of $5x-1$.

$$5x^{3}-x^{2}-60x^{2}+12x+180x-36$$

Combine $-x^{2}$ and $-60x^{2}$ to get $-61x^{2}$.

$$5x^{3}-61x^{2}+12x+180x-36$$

Combine $12x$ and $180x$ to get $192x$.

$$5x^{3}-61x^{2}+192x-36$$