Multiplication of Algebraic Expressions

Q.

If we add a monomial and binomial, then the answer can never be a monomial. State whether the statement given is True or False.

1. True
2. False

Q. If abc = 1, then find the value of:

$\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}$ [4 MARKS]

Q.

Question 2 (ix)

Add:

ab - 4a, 4b - ab, 4a - 4b

Q.

The product of a monomial and a binomial is a:

1. Monomial

2. Trinomial

3. Binomial

4. Constant

Q.

Q.

A monomial multiplied by a monomial always gives a___.

Q.

Value of 2xy when x = 4 and y = 0 is ___

Q.

Q. Simplify the following algebraic expression by removing grouping symbols.
$2a–[4b–\{4a–3(2a–b)\left\}\right]$

Q.

Akash has 6xy+4x$y^2$ chocolates. He wants to distribute them to 2x children. How many chocolates does each of the child get if y=2?

___

Q.

Find the common factor of the expression: $6x^3{y}^4{z}^5+9x^5{y}^2{z}^6+24x^2{y}^7{z}^4$.

1. 6x³y²z²

2. 3x²y²z⁴

3. 2x³y²z⁴

4. 3x⁵y⁷z⁵

Q.

The product of two numbers is $-14m^6{n}^3-21m^4{n}^5+7m^5{n}^4$. If one number is $7m^2{n}^2$, then the other number is

1. $-2m^{4}n-3m^2{n}^3+m^3{n}^2$

2. $2m^{4}n-3m^2{n}^3+m^3{n}^2$

3. $-2m^{4}n-3m^2{n}^3-m^3{n}^2$

4. $2m^{4}n+3m^2{n}^3+m^3{n}^2$

Q. Find the value of $(3x^2+5y^2)(4xy-5y)$, if $x=2$ and $y=3$.$\left[2Marks\right]$

Q.

The product of $7x-4y$ and $3x-7y$ is

1. + + 61xy

2. - - 61xy

3. + - 61xy

4. + - 37xy

Q.

What are the factors of $15xy+6x^2$?

1. $3x(5y+2x)$

2. $3(5y+2x)$

3. $3x(5+2x)$

4. $3x(5y+x)$

Q.

If x is multiplied by (-2) the result is -48. Is the integer 'x' positive or negative?

__

Q.

The common factors of $2xy+6y^2$ are:

1. 2

2. y

3. x + 3y

4. All of these

Q.

$(a+b+c)(a-b-c)$ = ______

1. $a^2-b^2+c^2-2ca$

2. $a^2+b^2-c^2-ca$

3. $a^2+b^2+c^2-bc$

4. $a^2-b^2-c^2-2bc$

Q. Multiply:

(1) (3y − 2) (y² − 5y + 7)

Q.

The product of two numbers is $x^2+x-2$. If one of the numbers is $x-1$, Then the other number is

1. $x+2$

2. $x-2$

3. $x+1$

4. $x-1$

Q.

$(a+b)(a-b)$ can be expressed as _____.

1. $a^2+b^2$

2. $a^2-b^2$

3. $ab$

4. $a^2-2ab$

Q.

The common factor in the expression $2x^2+4xy+8x$ is ___.

Q. $\mathrm{If}A=2x^2-y+3\mathrm{xy},B=x^2+2\mathrm{xy}\mathrm{and}C=3y+2\mathrm{xy},\mathrm{find}A-B+C.$

Q. Find the value of a:
5a-20 = 0

Q. $\frac{27x^{3}y}{9x^2}=$ ______.

1. $9x^{2}y$
2. $9x{y}^2$
3. $9xy$
4. $3xy$

Q.

Multiply:

(1) 3x by 4y

(2) 2y by 4y

(3) 8a by 4m

(4) −4x by 8x

(5) −5a by −8b

(6) −6p by 4pq

(7) 2a² by 5a²

(8) 3x²b² by 5x

(9) −7m²n² by 4m

(10) −5a²b by −7ab²

Q. Multiply (in vertical and horizontal arrangement):

(5) (5m²n – n²) × 4mn

Q.

The value of $(3x^2+5y^2)(4xy-5y)$, if $x=2$ and $y=3$ is $513$.

1. True

2. False

Q. Find the product of (x + 2) and (4y - 2).

1. 4xy+2x+8y+4
2. 4xy-2x+8y-4
3. 4xy+2x-8y+4
4. 4xy-2x-8y-4

Q. If we divide 5xyz + 3xy by xy, what will we get?

1. 5xy + 3
2. 5z + 4
3. 5z + 3
4. 5y + 6