Advertisements
Advertisements
Question
Simplify of the following:
(x+3)3 + (x−3)3
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
Write the following cube in expanded form:
(2x + 1)3
Evaluate the following using suitable identity:
(998)3
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Find the cube of the following binomials expression :
\[\frac{1}{x} + \frac{y}{3}\]
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
Evalute : `((2x)/7 - (7y)/4)^2`
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Find the squares of the following:
9m - 2n
Simplify by using formula :
(a + b - c) (a - b + c)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
Using suitable identity, evaluate the following:
1033
Using suitable identity, evaluate the following:
9992
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Expand the following:
`(4 - 1/(3x))^3`
