Advertisements
Advertisements
Question
Simplify of the following:
(x+3)3 + (x−3)3
Advertisements
Solution
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
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 8) (x – 10)
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Simplify (a + b + c)2 + (a - b + c)2
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If a + b = 8 and ab = 6, find the value of a3 + b3
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
Find the square of : 3a - 4b
Use identities to evaluate : (97)2
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
