Chapter 1.4, Problem 20PPE

To determine

To Evaluate: The expression $a^{2}bc-b^2$

Answer to Problem 20PPE

  $a^{2}bc-b^2=4080$

Explanation of Solution

Given information:

The expression $a^{2}bc-b^2$ and value of $a=8,b=4\&c=16$

Concept and Formula Used:

Rule of exponent and addition and subtraction.

  $a^n=a\times a\times a\times \mathrm{..................}n\text{ times}\text{.}$

BODMAS rule

Calculation:

The given expression is $a^{2}bc-b^2$

Putting the values of $a=8,b=4\&c=16$ in the expression

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

Conclusion:

  $a^{2}bc-b^2=4080$