Solve 1-2 identity Find the lfloor 9 2 + 3h 4 )( a 2 + 3h 4 rfloor | 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

$$( \frac { 10 } { 2 } + \frac { 3 b } { 4 } ) ( \frac { 2 } { 2 } + \frac { 3 b } { 4 } )$$

Evaluate

$\frac{9b^{2}}{16}+\frac{9b}{2}+5$

Short Solution Steps

Divide $2$ by $2$ to get $1$.

$$\left(\frac{10}{2}+\frac{3b}{4}\right)\left(1+\frac{3b}{4}\right)$$

Divide $10$ by $2$ to get $5$.

$$\left(5+\frac{3b}{4}\right)\left(1+\frac{3b}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $5$ times $\frac{4}{4}$.

$$\left(\frac{5\times 4}{4}+\frac{3b}{4}\right)\left(1+\frac{3b}{4}\right)$$

Since $\frac{5\times 4}{4}$ and $\frac{3b}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{5\times 4+3b}{4}\left(1+\frac{3b}{4}\right)$$

Do the multiplications in $5\times 4+3b$.

$$\frac{20+3b}{4}\left(1+\frac{3b}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{4}{4}$.

$$\frac{20+3b}{4}\left(\frac{4}{4}+\frac{3b}{4}\right)$$

Since $\frac{4}{4}$ and $\frac{3b}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{20+3b}{4}\times \frac{4+3b}{4}$$

Multiply $\frac{20+3b}{4}$ times $\frac{4+3b}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20+3b\right)\left(4+3b\right)}{4\times 4}$$

Multiply $4$ and $4$ to get $16$.

$$\frac{\left(20+3b\right)\left(4+3b\right)}{16}$$

Apply the distributive property by multiplying each term of $20+3b$ by each term of $4+3b$.

$$\frac{80+60b+12b+9b^{2}}{16}$$

Combine $60b$ and $12b$ to get $72b$.

$$\frac{80+72b+9b^{2}}{16}$$

Expand

$\frac{9b^{2}}{16}+\frac{9b}{2}+5$

Short Solution Steps

Divide $2$ by $2$ to get $1$.

$$\left(\frac{10}{2}+\frac{3b}{4}\right)\left(1+\frac{3b}{4}\right)$$

Divide $10$ by $2$ to get $5$.

$$\left(5+\frac{3b}{4}\right)\left(1+\frac{3b}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $5$ times $\frac{4}{4}$.

$$\left(\frac{5\times 4}{4}+\frac{3b}{4}\right)\left(1+\frac{3b}{4}\right)$$

Since $\frac{5\times 4}{4}$ and $\frac{3b}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{5\times 4+3b}{4}\left(1+\frac{3b}{4}\right)$$

Do the multiplications in $5\times 4+3b$.

$$\frac{20+3b}{4}\left(1+\frac{3b}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{4}{4}$.

$$\frac{20+3b}{4}\left(\frac{4}{4}+\frac{3b}{4}\right)$$

Since $\frac{4}{4}$ and $\frac{3b}{4}$ have the same denominator, add them by adding their numerators.

$$\frac{20+3b}{4}\times \frac{4+3b}{4}$$

Multiply $\frac{20+3b}{4}$ times $\frac{4+3b}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(20+3b\right)\left(4+3b\right)}{4\times 4}$$

Multiply $4$ and $4$ to get $16$.

$$\frac{\left(20+3b\right)\left(4+3b\right)}{16}$$

Apply the distributive property by multiplying each term of $20+3b$ by each term of $4+3b$.

$$\frac{80+60b+12b+9b^{2}}{16}$$

Combine $60b$ and $12b$ to get $72b$.

$$\frac{80+72b+9b^{2}}{16}$$