Advertisements
Advertisements
प्रश्न
Simplify of the following:
(x+3)3 + (x−3)3
Advertisements
उत्तर
In the given problem, we have to simplify equation
Given (x+3)3 + (x−3)3
We shall use the identity `a^3 + b^3 = (a + b)(a^2+b^2 - ab)`
Here `a= (x+3),b= (x-3)`
By applying identity we get
` = (x+ 3+x - 3)[(x+ 3)^2 + (x-3)^2 - (x+ 3)(x-3)]`
` = 2x[(x^2 + 3^2 + 2 xx x xx 3) + (x^2 + 3^2 - 2 xx x xx 3) -(x^2-3^2)]`
` = 2x [(x^2+ 9 + 6x) + (x^2 + 9 - 6 x)-(x^2 - 3^2)]`
` = 2x[x^2 + 9 + 6x + x^2 + 9 -6x - x^2 + 9]`
`= 2x [x^2 + x^2 - x^2 - 6x + 6x+ 9 + 9 + 9]`
` = 2x [x^2 + 27]`
` = 2x^3 + 54x`
Hence simplified form of expression`(x+3)^3 +(x-3)^3`is `2x^3 + 54x`.
APPEARS IN
संबंधित प्रश्न
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate following using identities:
991 ☓ 1009
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
Evaluate of the following:
1043 + 963
If `x - 1/x = 3 + 2sqrt2`, find the value of `x^3 - 1/x^3`
Find the following product:
(2ab − 3b − 2c) (4a2 + 9b2 +4c2 + 6 ab − 6 bc + 4ca)
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
Use the direct method to evaluate the following products:
(5a + 16) (3a – 7)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
Expand the following:
(x - 3y - 2z)2
Simplify by using formula :
(x + y - 3) (x + y + 3)
If x + y = 9, xy = 20
find: x2 - y2.
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Using suitable identity, evaluate the following:
101 × 102
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
