Q49. - Algebra 1

Question

Evaluate the expression $a^{2}bc-b^2$ if $a=8,b=4,c=16$.

Step-by-Step Solution

Answer

The value of the expression $a^{2}bc-b^2$ is 4080.

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  where  can be written as

$\begin{array}{l}5b-2ac=5\left(4\right)-2\left(3\right)\times 1\\ =(5\times 4)-(2\times 3)\times 1\\ =20-(6\times 1)\\ =20-6\\ =14\end{array}$

Step 3. DESCRIPTION OF STEP.

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

$\begin{array}{l}{a}^{2}bc-b^2=8^2\cdot 4\cdot 16-4^2\\ \text{Evaluate the powers }{8}^2\&4^2\\ a^{2}bc-b^2=64\cdot 4\cdot 16-16\\ \text{Multiply 64,4\&16}\\ a^{2}bc-b^2=4096-16\\ \text{Subtract 16 from 4096}\\ a^{2}bc-b^2=4080\end{array}$