Advertisements
Advertisements
Question
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
Options
10000
6250
7500
3750
Advertisements
Solution
We have to find the product of `75xx75+2xx75 xx 25+25 xx 25`
Using identity `(a+b)^2 = a^2 + 2ab +b^2`
`(a+b)^2 = a xx a +2 xx b +b xx b`
Here ` a = 75 , b = 25
`(75+25)^2 = 75 xx 75 +2 xx 75 xx 25 +25 xx 25`
`(100)^2 = 75 xx 75 +2 xx 75 xx 25+ 25xx 25`
`10000 = 75 xx 75 +2 xx 75 xx 25 +25 xx 25`
Hence the product of `75 xx 75 +2 xx 75 xx 25 +25 xx 25` is 10,000 .
APPEARS IN
RELATED QUESTIONS
Evaluate the following using suitable identity:
(998)3
Factorise the following:
8a3 + b3 + 12a2b + 6ab2
Simplify the following products:
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
Write the expanded form:
`(-3x + y + z)^2`
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If a + b = 8 and ab = 6, find the value of a3 + b3
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
Find the following product:
(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
(a − b)3 + (b − c)3 + (c − a)3 =
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Evaluate: (2a + 0.5) (7a − 0.3)
Expand the following:
(m + 8) (m - 7)
Expand the following:
(2p - 3q)2
If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
The coefficient of x in the expansion of (x + 3)3 is ______.
Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a – 3.
