The Factors Of X3 −X2y − Xy2 + Y3 Are - Mathematics

Advertisements
Advertisements
MCQ

The factors of x3 −x2y − xy2 + y3 are

Options

  • (x + y) (x2 − xy + y2)

  • (x + y) (x2 + xy + y2)

  • (x + y)2 (x − y)

  • (x − y)2 (x + y)

Advertisements

Solution

The given expression to be factorized is

 x3 −x2y − xy2 + y3 

Take common  `x^2` from the first two terms and `-y^2` from the last two terms. That is

 x3 −x2y − xy2 + y3 ` = x^2 (x-y) - y^2 (x-y)`

Finally, take common (x-y)from the two terms. That is

x3 −x2y − xy2 + y3  = `(x-y)(x^2 - y^2)`

                             ` = (x-y){(x)^2 - (y)^2 }`

                             ` = (x- y)(x+y)(x-y)`

                             ` = (x-y)^2 (x+y)`

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.6 [Page 25]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.6 | Q 1 | Page 25

RELATED QUESTIONS

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

The number z multiplied by itself.


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: `a^2 x^2 + (ax^2 + 1)x + a`


Factorize `9(2a - b)^2 - 4(2a - b) - 13`


Factorize the following expressions:

x3y3 + 1


Factorize the following expressions: 

a12 + b12


`3sqrt3a^3 - b^3 - 5sqrt5c^3 - 3sqrt15abc`


If x + y = 4 and xy = 2, find the value of x2 + y2


If 3x + 5y = 11 and xy = 2, find the value of 9x2 + 25y2


Find the value of the following expression: 16x2 + 24x + 9, when \[x = \frac{7}{4}\]


Find the value of the following expression:  64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]


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


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


Write the value of 483 − 303 − 183.


Factorize: x4 + x2 + 25.


The expression (a − b)3 + (− c)3 + (c −a)3 can be factorized as


The expression x4 + 4 can be factorized as


If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2, then k =


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


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


Multiply: (x - a)(x + 3b)


Divide: 8x + 24 by 4


Divide: - 50 + 40p by 10p


Divide: 12x3y - 8x2y2 + 4x2y3 by 4xy 


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


Divide: 2a2 - 11a + 12 by a - 4 


Divide: 8a2 + 4a - 60 by 2a - 5 


Divide: 35a3 + 3a2b - 2ab2 by 5a - b 


Divide: 10x3y - 9xy2 - 4x2y2 by xy 


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.


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.


Express the following as an algebraic expression:

Sum of p and 2r – s minus sum of a and 3n + 4x.


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 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


Write the variables, constant and terms of the following expression

b + 2


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


An algebraic statement which is equivalent to the verbal statement “Three times the sum of ‘x’ and ‘y’ is


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


In a polynomial, the exponents of the variables are always ______.


Which of the following is correct?


An equation is true for all values of its variables.


–b – 0 is equal to ______.


If Rohit has 5xy toffees and Shantanu has 20yx toffees, then Shantanu has ______ more toffees.


A taxi service charges ₹ 8 per km and levies a fixed charge of ₹ 50. Write an algebraic expression for the above situation, if the taxi is hired for x km.


Shiv works in a mall and gets paid ₹ 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.


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.


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.

Commutative property of multiplication


Share
Notifications



      Forgot password?
Use app×