###### Advertisements

###### Advertisements

Mark the correct alternative in each of the following: The factors of a^{2} − 1 − 2x − x^{2} are

#### Options

(a − x + 1) (a − x − 1)

(a + x − 1) (a − x + 1)

` (a+x+1)(a- x -1)`

none of these

###### Advertisements

#### Solution

The given expression to be factorized is `a^2 - 1 -2x - x^2`

Take common -1from the last three terms and then we have

a^{2} − 1 − 2x − x^{2 }` = a^2 - (1 + 2x + x^3)`

`= a^2 - {(1)^2 + 2.1.x + (x)^2}`

` = a^2 - (1+x)^2`

` = (a)^2 - (1 + x)^2`

` = {a+ (1+x)}{ a-(1+x)}`

`= (a+1 + x)(a-1-x)`

` = (a+x+1)(a- x -1)`

#### APPEARS IN

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

Product of numbers y and z subtracted from 10.

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

Factorize a^{2} - b^{2} + 2bc - c^{2}

Factorize a^{2} + 4b^{2} - 4ab - 4c^{2}

Factorize 8x^{3} + 27 y^{3} + 36x^{2} y + 54xy^{2}

Factorize 8a^{3}^{ }+ 27b^{3} + 36a^{2}b + 54ab^{2}

Factorize 8a^{3} – 27b^{3} – 36a^{2}b + 54ab^{2}

`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 x^{2} + y^{2}

If 3x + 5y = 11 and xy = 2, find the value of 9x^{2}^{ }+ 25y^{2}

Find the value of the following expression: 64x^{2} + 81y^{2} + 144xy, when x = 11 and \[y = \frac{4}{3}\]

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

If x^{2} + y^{2} = 29 and xy = 2, find the value of *x + y.*

If x^{2} + y^{2} = 29 and xy = 2, find the value of *x - y.*

If x^{2} + y^{2} = 29 and xy = 2, find the value of *x*^{4} + *y*^{4 }.

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

4*x*^{2}^{ }− 20*x* + 20

27*x*^{3} − *y*^{3} − *z*^{3} − 9*xyz*

(x + y)^{3} − (x − y)^{3} can be factorized as

The factors of x^{4} + x^{2} + 25 are

**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 3y^{2}z ÷ 4x

Write the number of the term of the following polynomial.

5x^{2} + 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, xy^{2}, 3y^{2} − 5y + 8, 9x − 3x^{2} + 15x^{3} − 7,

3x × 5y, 3x ÷ 5y, 2y ÷ 7 + 3x − 7 and 4 − ax^{2} + bx + y

Evaluate: (a^{2} + 2ab + b^{2})(a + b)

Evaluate: (4m - 2)(m^{2} + 5m - 6)

Evaluate: (8 - 12x + 7x^{2} - 6x^{3})(5 - 2x)

Evaluate: (a^{2} + b^{2} + c^{2} - ab - bc - ca)(a + b + c)

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

Multiply: (3x - 5y + 2)(5x - 4y - 3)

Multiply: (1 + 6x^{2} - 4x^{3})(-1 + 3x - 3x^{2})

Divide: 8x + 24 by 4

Divide: m^{2} - 2mn + n^{2} by m - n

Divide: x^{2} + 4xy + 4y^{2} by x + 2y

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.

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.

**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 x^{2} and x in the following polynomials

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

Write the coefficient of x^{2} and x in the following polynomials

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

Write the coefficient of x^{2} and x in the following polynomials

πx^{2} – x + 2

Write the coefficient of x^{2} and x in the following polynomials

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

Write the coefficient of x^{2} and x in the following polynomials

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

Complete the table.

× | 2x^{2} |
−2xy | x^{4}y^{3} |
2xyz | (___)xz^{2} |

x^{4} |
|||||

(___) | 4x^{5}y^{4} |
||||

−x^{2}y |
|||||

2y^{2}z |
−10xy^{2}z^{3} |
||||

−3xyz | |||||

(___) | −14xyz^{2} |

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 _________

Write the variables, constant and terms of the following expression

18 + x – y

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”.

3p^{2} – 5pq + 2q^{2} + 6pq – q^{2} + pq is a

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

The value of 3x^{2} – 5x + 3 when x = 1 is ______.

In the formula, area of circle = πr^{2}, the numerical constant of the expression πr^{2} is ______.

The total number of planets of Sun can be denoted by the variable n.

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?

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

Commutative property of addition

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

Associative property of addition

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

Distributive property of multiplication over addition