Chapter ISG, Problem 8.7.1.4P

a.

To determine

To simplify expression

Answer to Problem 8.7.1.4P

  $y^2{z}^2\{(11x{y}^{2}z-4)(11x{y}^{2}z+4)\}$

Explanation of Solution

Given:

  $121x^2{y}^6{z}^4-16y^2{z}^2$

Calculation:

From the given term, taking out common

  = $y^2{z}^2(121x^2{y}^4{z}^2-16)$

Rewriting the expression = $y^2{z}^2\{{(11)}^2{x}^2{y}^4{z}^2-{(4)}^2\}$$(\because 121={11}^2,16=4^2)$

So, = $y^2{z}^2\{{(11x{y}^{2}z)}^2-{(4)}^2\}$

Using identity $a^2-b^2=(a+b)(a-b)$

  = $y^2{z}^2\{(11x{y}^{2}z-4)(11x{y}^{2}z+4)\}$

b.

To determine

To simplify the expression

Answer to Problem 8.7.1.4P

  $98200$

Explanation of Solution

Given:

  ${991}^2-81$

Calculation:

We know that, $81=9^2$

Substituting value,

  ${991}^2-9^2$

Using identity $a^2-b^2=(a+b)(a-b)$

  = $(991-9)(991+9)$

So,

  = $(982)(100)$

Solving equation,

  = $98200$