[X/2 + Y + Z/3]^3 + [X/2 + (2y)/3 + Z]^3 + [-(5x)/6 - Y/3 - (4z)/3] - Mathematics

Advertisements
Advertisements
Answer in Brief

`(x/2 + y + z/3)^3 + (x/2 + (2y)/3 + z)^3 + (-(5x)/6 - y/3 - (4z)/3)^3`

Advertisements

Solution

Let `(x/2 + y + z/3) = a, (x/3 - (2y)/3 + z) = b,  (-(5x)/6 - y/3 - (4z)/3) = c`

`a + b + c = x/2 + y + z/3 + x/3 - (2y)/3 + z - (5x)/6 - y/3 - (4z)/3`

`a + b + c = (x/2 + x/3 - (5x)/6) + (y - (2y)/3 - y/3) + (z/3 + z - (4z)/3)`

`a + b + c = (3x)/6 + (2x)/6 - (5x)/6 + (3y)/3 - (2y)/3 - y/3 + z/3 + (3z)/3 - (4z)/3`

`a + b + c = (5x - 5x)/6 + (3y - 3y)/3 + (4z - 4z)/3`

a + b + c = 0

∵ a + b + c = 0     `∴ a^3 + b^3 + c^3 = 3abc`

`∴ [x/2 + y + z/3]^3 + [x/3 - (2y)/3 + z]^3 + [-(5x)/6 - y/3 - (4z)/3]^3 = 3(x/2 + y + z/3)(x/3 - (2y)/3 + z)(-(5x)/6 - y/3 - (4z)/3)`

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.4 [Page 23]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.4 | Q 11 | Page 23

RELATED QUESTIONS

Get the algebraic expression in the following case using variables, constants and arithmetic operations.

Numbers x and y both squared and added.


Get the algebraic expression in the following case using variables, constants and arithmetic operations.

Number 5 added to three times the product of numbers m and n.


Factorize a2 + 2ab + b2 - c2


Factorize `x^2 + 12/35 x + 1/35`


Factorize `21x^2 - 2x + 1/21`


Factorize 2( x + y)2 - 9( x + y) - 5


Factorize the following expressions:

(a + b)3 – 8(a – b)3


Factorize the following expressions: 

( x + 2)3 + ( x - 2)3


Factorize the following expressions:

1029 – 3x3


Factorize the following expressions:

x3y3 + 1


Factorize  8a3 – 27b3 – 36a2b + 54ab2


`1/27 x^3 - y^3 + 125z^3 + 5xyz`


If \[x^2 + \frac{1}{x^2} = 18,\]  find the values of \[x + \frac{1}{x} \text { and } x - \frac{1}{x} .\]


If x − y = 7 and xy = 9, find the value of x2 + y2


Find the value of the following expression:  81x2 + 16y2 − 72xy, when \[x = \frac{2}{3}\] and  \[y = \frac{3}{4}\]


If x2 + y2 = 29 and xy = 2, find the value of x4 + y4 .


What must be added to the following expression to make it a whole square? 

4x2 − 12x + 7


What must be added to the following expression to make it a whole square? 

4x2 − 20x + 20


Separate the constants and variables from the following :

`-7,7+"x",7"x"+"yz",sqrt5,sqrt("xy"),(3"yz")/8,4.5"y"-3"x",`

8 −5, 8 − 5x, 8x −5y × p and 3y2z ÷ 4x


Write the number of the term of the following polynomial.

5x2 + 3 x ax


Write the number of the term of the following polynomial.

ax ÷ 4 – 7


Write the number of the term of the following polynomial.

ax – by + y x z


Write the number of the term of the following polynomial.

23 + a x b ÷ 2


Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :

8 − 3x, xy2, 3y2 − 5y + 8, 9x − 3x2 + 15x3 − 7,
3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax2 + bx + y


Evaluate: (8 - 12x + 7x2 - 6x3)(5 - 2x)


Multiply: (2x - 3y)(2x + 3y)


Multiply: (2x + 5y + 6)(3x + y - 8)


Multiply: (6x - 2y)(3x - y)


Divide: - 50 + 40p by 10p


Divide: 9a4b - 15a3b2 + 12a2b3 by - 3a2


The area of a rectangle is 6x2 – 4xy – 10y2 square unit and its length is 2x + 2y unit. Find its breadth.


Divide: 2m3n5 by - mn 


Divide: 6x2 - xy - 35y2 by 2x - 5y 


Divide: x3 - 6x2 + 11x - 6 by x2 - 4x + 3 


Write in the form of an algebraic expression:

Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).


Write in the form of an algebraic expression:

Perimeter (P) of a square is four times its side.


Write in the form of an algebraic expression:

Area of a square is square of its side.


Write in the form of an algebraic expression:

Surface area of a cube is six times the square of its edge.


Express the following as an algebraic expression:

The sum of x and y minus m.


Express the following as an algebraic expression:

The product of x and y divided by m.


Express the following as an algebraic expression:

The subtraction of 5m from 3n and then adding 9p to it.


Express the following as an algebraic expression:

The product of 12, x, y and z minus the product of 5, m and n.


Construct a formula for the following:

Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.


Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7; find the value of s.


Solve the following equation.

4(​x + 12) = 8 


Solve the following equation.

3y + 4 = 5y - 6


Choose the right answer from the option.

The simplest form of 5 ÷ `(3/2) - 1/3` is _______.


Choose the right answer from the option.

The solution of the equation `"3x" - 1/2 = 5/2 + "x"` is _____.


Choose the right answer from the option.

Which of the following expressions has the value 37?


Write the coefficient of x2 and x in the following polynomials

`4 + 2/5x^2 - 3x`


Write the coefficient of x2 and x in the following polynomials

`6 - 2x^2 + 3x^3 - sqrt(7)x`


Write the coefficient of x2 and x in the following polynomials

πx2 – x + 2


Write the coefficient of x2 and x in the following polynomials

`sqrt(3)x^2 + sqrt(2)x + 0.5`


Write the coefficient of x2 and x in the following polynomials

`x^2 - 7/2 x + 8`


Complete the table.

× 2x2 −2xy x4y3 2xyz (___)xz2
x4          
(___)     4x5y4    
−x2y          
2y2z         −10xy2z3
−3xyz          
(___)       −14xyz2  

The largest number of the three consecutive numbers is x + 1, then the smallest number is ________


The variable in the expression 16x – 7 is __________


The constant term of the expression 2y – 6 is _________


When y = –1, the value of the expression 2y – 1 is 3


Write the variables, constant and terms of the following expression

18 + x – y


Write the variables, constant and terms of the following expression

7p – 4q + 5


Write the variables, constant and terms of the following expression

29x + 13y


If x = 2 and y = 3, then find the value of the following expressions

2x – 3y


If x = 2 and y = 3, then find the value of the following expressions

x + y


If x = 2 and y = 3, then find the value of the following expressions

4y – x


If x = 2 and y = 3, then find the value of the following expressions

x + 1 – y


The value of 7a – 4b when a = 3, b = 2 is


Give an algebraic equation for the following statement:

“The difference between the area and perimeter of a rectangle is 20”.


3p2 – 5pq + 2q2 + 6pq – q2 + pq is a


Which of the following is correct?


Number of terms in the expression a2 + bc × d is ______.


An equation is true for all values of its variables.


The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.


The value of 3x2 – 5x + 3 when x = 1 is ______.


Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.


A school has a rectangular playground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?


The rate of planting the grass is ₹ x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.


In the given figure, the length of a green side is given by g and that of the red side is given by p.


Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together.


Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for ₹ 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?


Will the value of 11x for x = –5 be greater than 11 or less than 11? Explain.


Express the following properties with variables x, y and z.

Distributive property of multiplication over addition


Share
Notifications



      Forgot password?
Use app×