Solve (10x + y)(3x + 2y) - (5x - 4y)(- x - 6y) | 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

$$(10x+y)(3x+2y)-(5x-4y)(-x-6y)$$

Evaluate

$35x^{2}+49xy-22y^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $10x+y$ by each term of $3x+2y$.

$$30x^{2}+20xy+3yx+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Combine $20xy$ and $3yx$ to get $23xy$.

$$30x^{2}+23xy+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Apply the distributive property by multiplying each term of $5x-4y$ by each term of $-x-6y$.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy-4y\left(-x\right)+24y^{2}\right)$$

Multiply $-4$ and $-1$ to get $4$.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy+4yx+24y^{2}\right)$$

Combine $-30xy$ and $4yx$ to get $-26xy$.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-26xy+24y^{2}\right)$$

To find the opposite of $5x\left(-x\right)-26xy+24y^{2}$, find the opposite of each term.

$$30x^{2}+23xy+2y^{2}-5x\left(-x\right)-\left(-26xy\right)-24y^{2}$$

Multiply $-5$ and $-1$ to get $5$.

$$30x^{2}+23xy+2y^{2}+5xx-\left(-26xy\right)-24y^{2}$$

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

$$30x^{2}+23xy+2y^{2}+5x^{2}-\left(-26xy\right)-24y^{2}$$

Combine $30x^{2}$ and $5x^{2}$ to get $35x^{2}$.

$$35x^{2}+23xy+2y^{2}-\left(-26xy\right)-24y^{2}$$

The opposite of $-26xy$ is $26xy$.

$$35x^{2}+23xy+2y^{2}+26xy-24y^{2}$$

Combine $23xy$ and $26xy$ to get $49xy$.

$$35x^{2}+49xy+2y^{2}-24y^{2}$$

Combine $2y^{2}$ and $-24y^{2}$ to get $-22y^{2}$.

$$35x^{2}+49xy-22y^{2}$$

Expand

$35x^{2}+49xy-22y^{2}$

Solution Steps

Apply the distributive property by multiplying each term of $10x+y$ by each term of $3x+2y$.

$$30x^{2}+20xy+3yx+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Combine $20xy$ and $3yx$ to get $23xy$.

$$30x^{2}+23xy+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Apply the distributive property by multiplying each term of $5x-4y$ by each term of $-x-6y$.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy-4y\left(-x\right)+24y^{2}\right)$$

Multiply $-4$ and $-1$ to get $4$.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy+4yx+24y^{2}\right)$$

Combine $-30xy$ and $4yx$ to get $-26xy$.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-26xy+24y^{2}\right)$$

To find the opposite of $5x\left(-x\right)-26xy+24y^{2}$, find the opposite of each term.

$$30x^{2}+23xy+2y^{2}-5x\left(-x\right)-\left(-26xy\right)-24y^{2}$$

Multiply $-5$ and $-1$ to get $5$.

$$30x^{2}+23xy+2y^{2}+5xx-\left(-26xy\right)-24y^{2}$$

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

$$30x^{2}+23xy+2y^{2}+5x^{2}-\left(-26xy\right)-24y^{2}$$

Combine $30x^{2}$ and $5x^{2}$ to get $35x^{2}$.

$$35x^{2}+23xy+2y^{2}-\left(-26xy\right)-24y^{2}$$

The opposite of $-26xy$ is $26xy$.

$$35x^{2}+23xy+2y^{2}+26xy-24y^{2}$$

Combine $23xy$ and $26xy$ to get $49xy$.

$$35x^{2}+49xy+2y^{2}-24y^{2}$$

Combine $2y^{2}$ and $-24y^{2}$ to get $-22y^{2}$.

$$35x^{2}+49xy-22y^{2}$$