Factorize the Following Expressions: X3 + 6x2 +12x +16 - Mathematics

Advertisements
Advertisements

Factorize the following expressions:

x3 + 6x2 +12x +16

Advertisements

Solution

= x3 + 6x2 +12x + 8 + 8

= x3 + 3 × x2 × 2 + 3 × x × 22 + 23 + 8

= ( x = 2)3 + 8              [ ∵ a3 + 3a2b + 3ab2 + b3 = (a + b)3

= ( x + 2)3 + 23

= ( x + 2 + 2)(( x + 2)2  - 2 ( x + 2) + 22 )  [∵ a3 + b3  = (a + b)(a2 - ab + b2 ) ]

= ( x + 4)(x2 + 4x + 4 - 2x - 4 + 4)             [∵ (a + b)2 = a2 + 2ab + b2]

= ( x + 4)(x2  + 2x + 4)

∴ x3  + 6x2  +12x +16 = ( x + 4)(x2  + 2x + 4)

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.2 [Page 14]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.2 | Q 21 | Page 14

RELATED QUESTIONS

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

Subtraction of z from y


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

One-half of the sum of numbers x and y.


Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

One-fourth of the product of numbers p and q.


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.

Product of numbers y and z subtracted from 10.


Factorize: `a^2 x^2 + (ax^2 + 1)x + a`


Factorize x( x - 2)( x - 4) + 4x - 8


Factorize  a2 + 4b2 - 4ab - 4c2


Factorize xy9 - yx9


Factorize x4 + x2 y2 + y4


Factorize  a3 – 3a2b + 3ab2 – b3 + 8


Factorize  8a3 – 27b3 – 36a2b + 54ab2


x3 - 8y3 + 27z3 +18xyz


(a – 3b)3 + (3b – c)3 + (c – a)3


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


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


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


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


If x2 + y2 = 29 and xy = 2, find the value of x + y.


If x2 + y2 = 29 and xy = 2, find the value of x - y.


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 − 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: (c + 5)(c - 3)


Evaluate: `(1/2 "a" + 1/2 "b") (1/2 "a" - 1/2 "b")`


Evaluate: (3x - 1)(4x3 - 2x2 + 6x - 3) 


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


Divide: 25x2y by - 5y2 


Divide: - 50 + 40p by 10p


Divide: 10a3 - 15a2b by - 5a2 


Divide: m2 - 2mn + n2 by m - n 


Divide: 6x3 + 5x2 - 21x + 10 by 3x - 2 


Divide: m3 - 4m2 + m + 6 by m2 - m - 2 


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 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


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

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


3p2 – 5pq + 2q2 + 6pq – q2 + pq is a


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.


–b – 0 is equal to ______.


In the formula, area of circle = πr2, the numerical constant of the expression πr2 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 student wrote an algebraic expression for “5 less than a number n divided by 3” as `n/3 - 5`. What error did the student make?


Match Column I with Column II in the following:

Column I Column II
1. The difference of 3 and a number squared (a) 4 – 2x
2. 5 less than twice a number squared (b) n2 – 3
3. Five minus twice the square of a number (c) 2n2 – 5
4. Four minus a number multiplied by 2 (d) 5 – 2n2
5. Seven times the sum of a number and 1 (e) 3 – n2
6. A number squared plus 6 (f) 2(n + 6)
7. 2 times the sum of a number and 6 (g) 7(n + 1)
8. Three less than the square of a number (h) n2 + 6

Share
Notifications



      Forgot password?
Use app×