Advertisements
Advertisements
प्रश्न
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
Advertisements
उत्तर
In the given problem, we have to simplify equation
Given (2x − 5y)3 − (2x + 5y)3
We shall use the identity `a^3 - b^3 = (a-b)(a^2+ b^2 + ab)`
Here ` a= (2x - 5y), b = (2x + 5y)`
By applying the identity we get
` = (2x - 5y - 2x 5y)[(2x - 5y)^2 +(2x + 5y)^2 + ((2x - 5y) xx (2x + 5y))]`
` = ( 2x - 5y - 2x - 5y)[(2x xx 2x + 5y xx 5y - 2 xx 2x xx 5y) + (2x xx 2x + 5yxx 5y + 2 xx 2x xx 5y) + ( 4x^2 - 25y^2)]`
` = ( - 10y)[(4x^2 + 25y^2 - 20xy)+ (4x^2 + 25y^2 + 20xy ) + 4x^2 + 25y^2 ]`
` = ( - 10y)[4x^2 + 25y^2 - 20xy+ 4x^2 + 25y^2 + 20xy + 4x^2 -25y^2 ]`
By rearranging the variable we get,
` = ( - 10y)[4x^2 + 4x^2 + 4x^2 + 25y^2]`
` = - 10y xx [12x^2 + 25y^2]`
`= -120x^2y - 250y^3`
Hence the simplified value of `2x - 5y^3 -(2x + 5y)^3`is `-120x^2y - 250y^3`.
APPEARS IN
संबंधित प्रश्न
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Write in the expanded form:
`(a + 2b + c)^2`
Write in the expanded form:
`(2 + x - 2y)^2`
Write in the expand form: `(2x - y + z)^2`
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Find the following product:
(7p4 + q) (49p8 − 7p4q + q2)
If a + b = 6 and ab = 20, find the value of a3 − b3
If a + b + c = 9 and ab +bc + ca = 26, find the value of a3 + b3+ c3 − 3abc
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
If a - b = 7 and ab = 18; find a + b.
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
Evaluate the following without multiplying:
(1005)2
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Which one of the following is a polynomial?
The coefficient of x in the expansion of (x + 3)3 is ______.
Factorise the following:
9y2 – 66yz + 121z2
