मराठी

Evaluate Following Using Identities: 991 ☓ 1009

Advertisements
Advertisements

प्रश्न

Evaluate following using identities:

991 ☓ 1009

Advertisements

उत्तर

In the given problem, we have to evaluate expressions by using identities.

The given expression is 991 x 1009

We have `(991 + 1009)/2 = 1000`

So we can express 991 and  1009 in the terms of 1000 as

991 = 1000 - 9

1009 = 1000 + 9

`991 xx 1009 = (1000 - 9)(1000 + 9)`

We shall use the identity  `(x - y)(x + y) = x^2 - y^2`

Here

(x - y) = (1000 - 9)

(x + y) = (1000 + 9)

By applying in identity we get 

`(1000 - 9)(1000 + 9) = (1000)^2 - (9)^2`

= 1000000 - 81

= 999919

Hence the value of 991 x 1009 is 999919

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Algebraic Identities - Exercise 4.1 [पृष्ठ ७]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 9
पाठ 4 Algebraic Identities
Exercise 4.1 | Q 2.3 | पृष्ठ ७

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Expand the following, using suitable identity:

(–2x + 5y – 3z)2


What are the possible expressions for the dimensions of the cuboids whose volume is given below?

Volume : 3x2 – 12x

Write in the expanded form:

`(a/(bc) + b/(ca) + c/(ab))^2`


Write in the expanded form: (-2x + 3y + 2z)2


Simplify of the following:

\[\left( \frac{x}{2} + \frac{y}{3} \right)^3 - \left( \frac{x}{2} - \frac{y}{3} \right)^3\]

Find the following product:

\[\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)\]

If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]


If x = 3 and y = − 1, find the values of the following using in identify:

\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]


If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =


If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is 


If a - b = 7 and ab = 18; find a + b.


Use the direct method to evaluate the following products :
(y + 5)(y – 3)


Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`


Expand the following:
(a + 4) (a + 7)


Simplify by using formula :
(5x - 9) (5x + 9)


Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401


Simplify:
(2x + y)(4x2 - 2xy + y2)


Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16


The value of 2492 – 2482 is ______.


If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×