x 3 27 + x 2 y 15 + xy 2 25 + y 3 125

x 3 27 + x 2 y 25 + xy 2 25 + y 3 125

x 3 25 + x 2 y 15 + xy 2 25 + y 3 125

x 3 27 + xy 15 + xy 2 25 + y 3 125

The value of 27 a 3 - 2 2 b 3 is equal to:

3 a - 2 b 9 a 2 + 2 b 2 + 3 2 ab

3 a - 2 b 9 a 2 + 2 b 2 + 6 2 ab

3 a - 2 b 9 a 2 - 2 b 2 - 3 2 ab

3 a - 2 b 9 a 2 - 2 b 2 + 6 2 ab

EASY

Earn 100

In the following question, two equations numbered I and II are given. You have to solve both questions and give answer among the following options.

(A) if $x > y$

(B) if $x \geq y$

(C) if $x < y$

(D) if $x \leq y$

(E) if $x = y$ or the relationship cannot be established.

$I . 4 x^{2} - 18 x + 18 = 0 II . 3 y^{2} + 5 y - 12 = 0$

50% studentsanswered this correctly

Important Questions on Expansion and Factorization

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

Which is the largest six-digit number, which when divided by

12, 15, 20, 24

and

30

, leaves the remainders

8, 11, 16, 20

and

26

respectively.

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

Expand

{(\frac{x}{3} + \frac{y}{5})}^{3}

HARD

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

When a number is successively divided by

3, 4

and

7

, the remainder obtained is

2, 3

and

5

, respectively. What will be the remainder when

42

divides the same number?

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

If the

5

-digit number

538 x y

is divisible by

3, 7

and

11

, then the value of

(x^{2} + y^{2})

is _____.

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

Two positive numbers differ by

2001

. When the larger number is divided by the smaller number, the quotient is

9

and the remainder is

41

. The sum of the digits of the larger number is:

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

1433 \times 1433 \times 1422 \times 1425

is divided by

12

, then what is the remainder?

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

2 x^{2} + y^{2} + 8 z^{2} - 2 \sqrt{2} xy + 4 \sqrt{2} yz - 8 zx = {(Ax + y + Bz)}^{2}

, then the value of

(A^{2} + B^{2} - AB)

is:

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

The sum of the zeroes of the polynomial $p (x) = 5 x^{2} + 2 x - 3$ is

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

The value of

27 a^{3} - 2 \sqrt{2} b^{3}

is equal to:

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

30 x^{2} - 15 x + 1 = 0

, then what is the value of

25 x^{2} + {(36 x^{2})}^{- 1}

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

Let

x

be the least number divisible by

13

, such that when

x

is divided by

4, 5, 6, 7, 8

and

12

, the remainder in each case is

2

. The sum of the digits of

x

is _____.

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

Find the remainder in the expression

\frac{557 \times 653 \times 672}{9}

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

When a number is successively divided by

3, 4

and

7

, the remainder obtained are

2, 3

and

5

respectively. What will be the remainder when

84

divided the same number?

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

When

3738, 5659

and

9501

are divided by the greatest possible number

x

, the remainder in each case is

y

. what is the sum of

x

and

y

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

The ratio of the divisor to the remainder is

3 : 2

and the ratio of the divisor to quotient is

7 : 12

. If the remainder is

14

, then the remainder when the dividend is divided by

9

is:

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

a, b, c

are real numbers

a^{2} + b^{2} + c^{2} = 1

, then the set of values

a b + b c + c a

can take is:

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

The degree of a quadratic polynomial is:

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

1 - 64 x^{3} - 12 x + {px}^{2} = {(1 - 4 x)}^{3}

, then the value of

p

is:

EASY

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

In a division sum, the divisor is

10

times the quotient and

5

times the remainder. If the remainder is

46

, the dividend is:

MEDIUM

Mathematics>Algebra>Expansion and Factorization>Factorization by Splitting the Middle Term

A student was asked to divide a number by

6

and add

12

to the quotient. He, however, first added

12

to the number and then divided it by

6

, getting

112

as the answer. The correct answer should have been _____.

In the following question, two equations numbered I and II are given. You have to solve both questions and give answer among the following options. (A) if x>y (B) if x≥y (C) if x<y (D) if x≤y (E) if x=y or the relationship cannot be established. I. 4x2-18x+18=0II. 3y2+5y-12=0

Important Questions on Expansion and Factorization

Learn and Prepare for any exam you want !