# Algebraic Identities Cubic Type Free Doubts and Solutions

### CBSE - IX - Mathematics - Polynomials

## Prove (a+b+c)^3 - a^3 - b^3 - c^3 = 3(a+b) (b+c) (c+a)

**kirtiagarwal148**7th June 2018, 7:49 PM

### CBSE - IX - Mathematics - Polynomials

## Without actually calculating the cubes,find the value of (1/2)^3+(1/3)^3-(5/6)^3

**Kalasashi88**31st May 2018, 11:32 PM

### CBSE - IX - Mathematics - Polynomials

a+b=6 and ab=8 then a=

**Prakash**18th March 2018, 5:02 PM

### CBSE - IX - Mathematics - Polynomials

Sir how can we expand alpha cube - beta cube

**rahmanfarseen**16th March 2018, 1:40 PM

### CBSE - IX - Mathematics - Polynomials

## iF a+b+c = 0, then prove that (b+c)2 / 3bc + (c+a)2 / 3ca + (a+b)2 / 3ab = 1

**Vikas**5th March 2018, 12:04 PM

### CBSE - IX - Mathematics - Polynomials

## actorize (x – 3y)3 + (3y – 7z)3 + (7z - x)3

**gujarsurjeet007**15th February 2018, 6:52 PM

### CBSE - IX - Mathematics - Polynomials

## Without actually calculating the cubes, find the value of (-1)^3 + (-2)^3 + (-3)^3 + (-4)^3 + 2(5^3) . Write the identify used

**Marie**9th February 2018, 4:29 PM

### CBSE - IX - Mathematics - Polynomials

## If (x+1/x)=9,then find the value of (x^3+1/x^3)

**rr5210887**4th February 2018, 9:27 PM

### CBSE - IX - Mathematics - Polynomials

## If 2x+3y=12 and xy=6find the value of 8x³+27y³

**Pratikshyapmuduli**31st January 2018, 10:44 PM

### CBSE - IX - Mathematics - Polynomials

## (x+y)3 + ( y + z)3 + ( z+x)3 - 3(x+y)(y+z)(z+x) = 2 ( x3 + y3 + z3 - 3xyz)

**Vikas**23rd January 2018, 11:07 PM

### CBSE - IX - Mathematics - Polynomials

## Please solve question no. 7 with proper explanation

**adityaahuja099**11th December 2017, 9:03 PM

### CBSE - IX - Mathematics - Polynomials

## Please solve this problem with proper explanation

**adityaahuja099**11th December 2017, 8:53 PM

### CBSE - IX - Mathematics - Polynomials

## Factorise : x6 +8y6 - z6 + 6x2y2z2

**Topperlearning User**7th August 2017, 3:36 PM

### CBSE - IX - Mathematics - Polynomials

## The volume of a cuboid is given by the algebraic expression ky2 - 6ky +8k . Find the possible expressions of the dimensions of the cuboid.

**Topperlearning User**7th August 2017, 3:35 PM

### CBSE - IX - Mathematics - Polynomials

## Factorise : a7b +ab7

**Topperlearning User**7th August 2017, 3:35 PM

### CBSE - IX - Mathematics - Polynomials

## What are the possible expressions for the dimensions of the cuboids whose volume is given by x3 - 3x2 - 9x - 5 ?

**Topperlearning User**7th August 2017, 3:35 PM

### CBSE - IX - Mathematics - Polynomials

## Without actually evaluating the cubes, find the value of: 153 - 63 - 93

**Topperlearning User**7th August 2017, 3:34 PM

### CBSE - IX - Mathematics - Polynomials

## Use suitable identities to Factorise 3 - 8y 3 - 62y+ 12y2

**Topperlearning User**7th August 2017, 3:32 PM

### CBSE - IX - Mathematics - Polynomials

## Use suitable identity to factorise 27p3 + 8q3 + 54p2q + 36p q2

**Topperlearning User**7th August 2017, 3:30 PM

### CBSE - IX - Mathematics - Polynomials

## Use suitable identity to evaluate (97)3

**Topperlearning User**7th August 2017, 3:30 PM

### CBSE - IX - Mathematics - Polynomials

## The volume of a cube is x3 - 15x2 + 75x - 125 cubic units. Find the dimensions of the cube if x = 15 units.

**Topperlearning User**7th August 2017, 3:29 PM

### CBSE - IX - Mathematics - Polynomials

## Without actually evaluating the cubes, find the value of: (8)3 + (5)3 + (-13)3

**Topperlearning User**7th August 2017, 3:29 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize: 64x3 - 125y3

**Topperlearning User**7th August 2017, 3:28 PM

### CBSE - IX - Mathematics - Polynomials

## Factorise: 27x3 + 8y3

**Topperlearning User**7th August 2017, 3:28 PM

### CBSE - IX - Mathematics - Polynomials

## Write (3x + 5y)3 in the expanded form

**Topperlearning User**7th August 2017, 3:28 PM

### CBSE - IX - Mathematics - Polynomials

## Q) Let f(x) be a cubic polynomial such that f(1)=1,f(2)=2,f(3)=3 and f(4)=16. Find the value of f(5).

**banerjee_milky**5th June 2017, 10:34 AM

### CBSE - IX - Mathematics - Polynomials

## <div>EVALUATE :</div> <div><img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=a5a35ea08036eff27603398064836547.png" alt="30 cubed plus space space 20 to the power of 3 space end exponent minus 50 to the power of 3 space space end exponent space W I T H O U T space A C T U A L L Y space C A L C U L A T I N G space T H E space C U B E S space W R I T E space T H E space I D E N T I T Y space U S E D" align="middle" /></div>

**Sunny**24th May 2017, 7:19 PM

### CBSE - IX - Mathematics - Polynomials

## x^2+y^2=60 and x-y=6,then find the value of x^3-y^3

**dollyjacob1976**12th August 2016, 1:31 PM

### CBSE - IX - Mathematics - Polynomials

## chapter 4 rd sharma class 9 cce mcq q7

**Darpan**22nd July 2016, 4:05 PM

### CBSE - IX - Mathematics - Polynomials

## If x+y+z=0 , then show that x cube +y cube + Z cube = 3XYZ

**Furi**20th June 2016, 5:21 PM

### CBSE - IX - Mathematics - Polynomials

1) Factorise by using middle term splitting

8^{3} + 27y^{3 }+ z^{3 _ }18yz

2) Find

(783)^{2/3}

Please explain step-by-step.

use cubic algebraic identities

^{3}+ 27y

^{3 }+ z

^{3 _ }18yz

^{2/3}

**stutagra**26th May 2016, 4:36 PM

### CBSE - IX - Mathematics - Polynomials

## <div>If <img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=95a8b688c6f25add2c2414eb6de218e8.png" alt="left parenthesis a plus b right parenthesis squared" align="middle" />=<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=8f44ec5aaa891ddc30e3fd8c15c42b03.png" alt="2 a squared" align="middle" />+<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=b1ccb57005715054499408ba911fcf98.png" alt="2 b squared" align="middle" />, show that a=b</div>

**Divyaa**29th October 2015, 7:35 PM

### CBSE - IX - Mathematics - Polynomials

## X^3+1/x^3=216 and find the value of x+1/x

**akashkumar2005**17th September 2015, 3:55 PM

### CBSE - IX - Mathematics - Polynomials

## May I know how to verify the expansion of [a+b+c]2?

**prakritiprakash12**14th June 2015, 10:34 AM

### CBSE - IX - Mathematics - Polynomials

## A^1/x=b^1/y=c^1/z and abc =1 find the value of x+y+z

**Shringoyal**1st May 2015, 4:55 PM

### CBSE - IX - Mathematics - Polynomials

## FROM WHERE a^3 + b^3 formula is derived?

**Ayush**3rd April 2015, 7:55 PM

### CBSE - IX - Mathematics - Polynomials

## <div><img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=ce4fa3dfb460ec006eec3beddd2b40c6.png" alt="open parentheses 42 close parentheses to the power of 3 space end exponent space minus space open parentheses 18 close parentheses cubed space minus open parentheses 24 close parentheses cubed space e v a l u a t e space i t space w i t h space b y space d o i n g space a c t u a l l y space c a l c u l a t i n g space c u b e s" align="middle" /></div>

**KALAPANA.KOTAK**19th September 2014, 7:10 PM

### CBSE - IX - Mathematics - Polynomials

## factorize the following :
3Ö3c^{3} +5Ö2c^{3}

^{}

3Ö3c^{3} +5Ö2c^{3}

^{}

**smpadvisory**17th September 2014, 6:14 PM

### CBSE - IX - Mathematics - Polynomials

##
If a^{?}+b^{?}+c^{?}=0, then (a+b+c)^{3}= 27abc. how

If a^{?}+b^{?}+c^{?}=0, then (a+b+c)^{3}= 27abc. how

**manavmansvi**31st August 2014, 7:44 PM

### CBSE - IX - Mathematics - Polynomials

## give me the proof of a^3+b^3.

**ARJUN**3rd August 2014, 12:48 PM

### CBSE - IX - Mathematics - Polynomials

## <div>EVALUATE UING IDENTITIES</div> <div><img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=efc88502851e7f8a70722995a6001f7b.png" alt="left parenthesis 99 right parenthesis cubed" align="middle" /></div>

**sujatashetty2000**16th July 2014, 6:59 AM

### CBSE - IX - Mathematics - Polynomials

## Factorise : (i) (8b3 - 1) (ii) (p3q3 + 343)

**Topperlearning User**10th July 2014, 1:30 PM

### CBSE - IX - Mathematics - Polynomials

## simplify
783 raised to the power of 2/3 = ?

**Umar**4th July 2014, 6:12 PM

### CBSE - IX - Mathematics - Polynomials

## (a) Find the value of 34 x 36 using suitable identify. (b) Simplify using identify:

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Without actually calculating the cubes, find the value of 753 - 253 - 503.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Expand: (a) (b)

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorise:

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If a - b = 7, a2 + b2 = 85 find a3 - b3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorise: a3 - b3 + 1 + 3ab.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Prove that (x+y)3 - (x - y)3 - 6y (x2 - y2) = 8y3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If a + b = 10 and a2 + b2 = 58, find the value of a3 + b3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If x + y + z = 1, xy + yz + zx = -1 and xyz = -1 find the value of x3+y3+z3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Without finding the cubes, factorize and find the value of:

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If (x + y + z) = 0, then prove that (x3 + y3 + z3) = 3xyz.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If a+b = 12 and ab= 27, find the value of a3+b3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Simplify: .

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize: a7 + ab6.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Prove that = 1.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If x + = 7 then find the value of x3 + .

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize :.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Evaluate using suitable identity (999)3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize : (x - y)3 + (y - z)3 + (z - x)3

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize : x3 - 8y3 - 27z3 - 18xyz.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If x3 + ax2 + bx + 6 has x - 2 as a factor and leaves a remainder 3 when divided by x - 3, find the values of a and b.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## The volume of a cube is given by the polynomial p(x) = 8x3 - 36x2 + 54x - 27. Find the possible expression for the sides of cube.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize : 8 - 27x3 - 36x + 54x2

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize : a3 + 8b3 - 27c2 + 18 abc.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If x and y be two positive real number such that 8x3 + 27y3 = 730 and 2x2y + 3xy2 = 15 then show that 2x + 3y = 10.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If x + y + z = 1, xy + yz + zx = -1 and xyz = -1 then find the value of x3 + y3 + z3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Using suitable identity evaluate (-28)3 + (9)3 + (19)3

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Using suitable identity evaluate (-32)3 + (18)3 + (14)3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Prove that: 2x3 + 2y3 + 2z3 - 6xyz = (x + y + z) [(x - y)2 + (y - z)2 + (z - x)2 hence evaluate 2(7)3 + 2(9)3 + 2(13)3 - 6(7) (9) (13).

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Using suitable identity evaluate (42)3 - (18)3 - (24)3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorize : 8 a3 - b3 - 12a2b + 6ab2

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If x = 2 + , then find the value of .

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If a + b = 8 and a2 + b2 = 40 find the value of a3 + b3=.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If p = 4 - q, prove that p3 + q3 + 12pq = 64.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Factorise : a3(b - c)3 + b3 (c - a)3 + c3 (a - b)3

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Verify x3 + y3 + z3 - 3xyz = (x + y + z) [(x - y)2 + (y - z)2 + (z - x)2] and factorise 64x3 - 125y3 - 64z3 + 240 xyz.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## If a = 1 - , find

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## Evaluate (999)3.

**Topperlearning User**4th June 2014, 1:23 PM

### CBSE - IX - Mathematics - Polynomials

## 27a3 + 1/64a2 +27a2/4b +9a/16b2

**sumvee2002**27th May 2014, 10:27 AM