Q51. - Algebra 1

Question

Evaluate the expression $\frac{2b+3c^2}{4a^2-2b}$ if $a=8,b=4,c=16$.

Step-by-Step Solution

Answer

The value of the expression of $\frac{2b+3c^2}{4a^2-2b}$ is $3\frac{4}{31}$.

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed division, by multiplication, addition, and finally subtraction.

Step 2. Example of applying BODMAS rule.

The expression $5b-\frac{2a}{c}$ where $a=3,b=4,c=2$ can be written as

$\begin{array}{l}5b-\frac{2a}{c}=5\left(4\right)-\frac{2\left(3\right)}{2}\\ =(5\times 4)-\frac{(2\times 3)}{2}\\ =20-3\\ =17\end{array}$

Step 3. DESCRIPTION OF STEP.

Substituting $a=8,b=4\text{ and c}=16$ in $\frac{2b+3c^2}{4a^2-2b}$

$\begin{array}{l}\frac{2b+3c^2}{4a^2-2b}=\frac{2\cdot 4+3\cdot {16}^2}{4\cdot 8^2-2\cdot 4}\\ \frac{2b+3c^2}{4a^2-2b}=\frac{2\cdot 4+3\cdot 256}{4\cdot 64-2\cdot 4}\end{array}$

$\begin{array}{l}\text{Multiply the powers 2\hspace{0.17em}\&\hspace{0.17em}4,\hspace{0.17em}3\hspace{0.17em}\&\hspace{0.17em}256,\hspace{0.17em}4\hspace{0.17em}\&\hspace{0.17em}64,\hspace{0.17em}2\hspace{0.17em}\&\hspace{0.17em}4}\\ \frac{2b+3c^2}{4a^2-2b}=\frac{8+768}{256-8}\end{array}$

$\begin{array}{l}\text{Add 8\hspace{0.17em}\&\hspace{0.17em}768 in numerator}\\ \frac{2b+3c^2}{4a^2-2b}=\frac{776}{256-8}\end{array}$

$\begin{array}{l}\text{Subtract 8 from 256 in denominator}\\ \frac{2b+3c^2}{4a^2-2b}=\frac{776}{248}=3\frac{4}{31}\end{array}$