Question

Evaluate using suitable identity 107^3

Answer 1

Answer:

1225043

Step-by-step explanation:

We are given or we have to evaluate

                                     $107^3$

using suitable identity.

since 107 can be written as 107 = 100+7

and       $107^3=(100+7)^3$

we know that the Identity

            $(a+b)^3=a^3+b^3+3ab(a+b)$

so, substitute a = 100 and b = 7 in above identity

we get

          $(100+7)^3=100^3+7^3+3(100)(7)(100+7)$

                          $=1000000+343+224700$

                          = 1225043

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Answer 2

Answer:

Using the identity, the simplified value of $107^3$ is 1225043.

Step-by-step explanation:

Recall the identity,

$(a+b)^3=a^3+b^3+3ab(a+b)$ . . . . . (1)

Step 1 of 1

Consider the given number as follows:

$107^3$ . . . . . (2)

Rewrite the number $107$ as the sum of $2$ numbers as follows:

107 = 100 + 7

Then, the expression (2) becomes,

$(100+7)^3$

Now,

Let $a=100$ and $b=7$.

Substitute the values 100 for $a$ and 7 for $b$ in the identity (1) as follows:

$(100+7)^3=100^3+7^3+3(100)(7)(100+7)$

Further, simplify the expression as follows:

$(100+7)^3=1000000+343+2100(100+7)$

                = 1000000 + 343 + 224700

                = 1225043

Final answer: Using the identity, the value of $107^3$ is 1225043.

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