Chapter 1.3, Problem 134E

  $\left(a\right)$

To determine

To calculate: The simplified form of the expression ${528}^2-{527}^2$ .

Answer to Problem 134E

The simplified form of the expression ${528}^2-{527}^2$ is $1055$ .

Explanation of Solution

Given information:

The expression ${528}^2-{527}^2$ .

Formula used:

The difference of square of two numbers a and b is $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Calculation:

Consider the expression ${528}^2-{527}^2$ .

Recall that the difference of square of two numbers a and b is $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Apply it,

  $\begin{array}{c}{528}^2-{527}^2=\left(528+527\right)\left(528-527\right)\\ =1055\left(1\right)\\ =1055\end{array}$

Thus, the simplified form of the expression ${528}^2-{527}^2$ is $1055$ .

  $\left(b\right)$

To determine

To calculate: The simplified form of the expression ${122}^2-{120}^2$ .

Answer to Problem 134E

The simplified form of the expression ${122}^2-{120}^2$ is $484$ .

Explanation of Solution

Given information:

The expression ${122}^2-{120}^2$ .

Formula used:

The difference of square of two numbers a and b is $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Calculation:

Consider the expression ${122}^2-{120}^2$ .

Recall that the difference of square of two numbers a and b is $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Apply it,

  $\begin{array}{c}{122}^2-{120}^2=\left(122+120\right)\left(122-120\right)\\ =242\left(2\right)\\ =484\end{array}$

Thus, the simplified form of the expression ${122}^2-{120}^2$ is $484$ .

  $\left(c\right)$

To determine

To calculate: The simplified form of the expression ${1020}^2-{1010}^2$ .

Answer to Problem 134E

The simplified form of the expression ${1020}^2-{1010}^2$ is $20300$ .

Explanation of Solution

Given information:

The expression ${1020}^2-{1010}^2$ .

Formula used:

The difference of square of two numbers a and b is $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Calculation:

Consider the expression ${1020}^2-{1010}^2$ .

Recall that the difference of square of two numbers a and b is $a^2-b^2=\left(a+b\right)\left(a-b\right)$ .

Apply it,

  $\begin{array}{c}{1020}^2-{1010}^2=\left(1020+1010\right)\left(1020-1010\right)\\ =2030\left(10\right)\\ =20300\end{array}$

Thus, the simplified form of the expression ${1020}^2-{1010}^2$ is $20300$ .

  $\left(d\right)$

To determine

To calculate: The simplified form of the expression $79\cdot 51$ .

Answer to Problem 134E

The simplified form of the expression $79\cdot 51$ is $4029$ .

Explanation of Solution

Given information:

The expression $79\cdot 51$ .

Formula used:

The special product of two numbers a and b is $\left(a+b\right)\left(a-b\right)=a^2-b^2$ .

Calculation:

Consider the expression $79\cdot 51$ .

Recall that the special product of two numbers a and b is $\left(a+b\right)\left(a-b\right)=a^2-b^2$ .

Apply it,

  $\begin{array}{c}79\cdot 51=\left(80-1\right)51\\ =80\left(51\right)-1\left(51\right)\\ =80\left(50+1\right)-51\\ =4000+\left(80-51\right)\end{array}$

Simplify it further as,

  $\begin{array}{c}79\cdot 51=4000+\left(80-51\right)\\ =4000+29\\ =4029\end{array}$

Thus, the simplified form of the expression $79\cdot 51$ is $4029$ .

  $\left(e\right)$

To determine

To calculate: The simplified form of the expression $998\cdot 1002$ .

Answer to Problem 134E

The simplified form of the expression $998\cdot 1002$ is $999996$ .

Explanation of Solution

Given information:

The expression $998\cdot 1002$ .

Formula used:

The special product of two numbers a and b is $\left(a+b\right)\left(a-b\right)=a^2-b^2$ .

Calculation:

Consider the expression $998\cdot 1002$ .

Recall that the special product of two numbers a and b is $\left(a+b\right)\left(a-b\right)=a^2-b^2$ .

Apply it,

  $\begin{array}{c}998\cdot 1002=\left(1000-2\right)\left(1000+2\right)\\ ={1000}^2-2^2\\ =1000000-4\\ =999996\end{array}$

Thus, the simplified form of the expression $998\cdot 1002$ is $999996$ .