Question

without actual multiplication,the value of(1001*1007)

Answer 1

It is easy...

1001 × 1007 ( Given )

= ( 1000+1 ) × ( 1000+7 )

Now, by using the identity

$x {}^{2} + (a + b)x + ab$

= $1000 {}^{2} + (1 + 7) \times 1000 + 1 \times 7$

= $1000000 + 8000 + 7$

= 1008007

Answer 2

The value of (1001×1007), is 1008007.

Given,

The expression: (1001×1007).

To find,

Value of the given expression without actual multiplication.

Solution,

Here, it can be seen that the given expression is,

1001×1007.

Let it be represented by p. That is,

p = 1001×1007.

To find the value, we can also write the above expression as,

p = (1000 + 1)×(1000 + 7).

Now, from one of the algebraic identities, we have,

$(x+a)(x+b)=x^{2} +(a+b)x+ab$

We can, on comparing the expression with the above identity assume, that here,

x = 1000,

a = 1, and,

b = 7.

Thus,

$p=(1000+1) \times (1000+7)=1000^{2} +(1+7) \times (1000)+(1) \times (7)$

$\implies p = 1000000 +(8) \times (1000)+7$

$\implies p = 1000000 + 8000+7$

$\implies p = 1008007.$

⇒ The value of the given expression = 1008007.

Therefore, the value of (1001×1007), is 1008007.

#SPJ2