Question

What is the value of $170 \times \left( { - 1} \right) \times \left( { - 170} \right) + 264 + 0$?

Answer 1

Hint: In the above problem, mention the multiplication sign, arithmetic operation, and also the integer square. The value will measure the number with the positive and negative sign included, we should know the rule of the product to solve this kind of problem.

Formula used:
Two positives make a positive,
$ + \times + = + $
Two negatives make a positive
$ - \times - = + $
A negative and a positive make a negative
$ - \times + = - $
A positive and a negative make a negative:
$ + \times - = - $
Where, is the positive sign, is the negative sign, and also represents the mathematical symbol of an integer, is representing the product of numbers.

Complete step-by-step answer:
Given by,
 Solve: $170 \times \left( { - 1} \right) \times \left( { - 170} \right) + 264 + 0$
We use the above formula,
Two negatives make a positive.
$ - \times - = + $
Refer the formula,
On simplifying as
We get,
$\Rightarrow$ $\left( { - 1} \right) \times \left( { - 170} \right) = 170$
Substituting the given value,
Here,
Put, $x = 170 \times 170 + 264 + 0$
Simplify the above equation,
let as consider $170 \times 170$ is ${170^2}$
We get,
$\Rightarrow$ $x = {170^2} + 264 + 0$
In addition,
We know that any number can add with zero makes that same number,
Simplifying the above equation, $264 + 0 = 264$
Apply the value in $x$ equation,
$\Rightarrow$ $x = {170^2} + 260$
Here we separate to find the value of ${170^2}$ is $28,900$
Substituting the given value,
We get,
$\Rightarrow$ $x = 28,900 + 264$
Simplifying the above equation,
$\Rightarrow$ $x = 29,164$
Hence, the value of $170 \times 170 + 264 + 0$ is $29,164$

Note: To split the problem into subproblems when multiplying the two or more numbers together and to perform the multiplication, using the multiplication table. The product of the two numbers is determined with a positive and negative sign and follows the rule of the product. To solve this type of problem, we should understand the multiplication table.