Algebraic Expression

Q.

Write $81$ as a product of prime factors.

Q. If x = 2, then find the value of 3x - 5.

1. -1
2. 2
3. 0
4. 1

Q. Choose the correct option based on the given statements.

Statement 1:- All identities are equations.
Statement 2:- All equations are identities.

1. Statement 1 is true but statement 2 is false.
2. Statement 2 is true but statement 1 is false.
3. Both the statements are true.
4. Both the statements are false.

Q.

4 times a certain number is as much as less than 60 as 7 times the number is greater than 61.Find the number

Q. How many terms are there in the expression $5xy+9yz+3zx+5x-4y$?

1. 6
2. 3
3. 4
4. 5

Q.

Which of the following is an example of binomial?

1. 2x² + x + 1

2. x⁴ + x - 1

3. -x + 1

4. 3x

Q. A polynomial is an algebraic expression in which variables are raised to only whole numbered powers.

1. True
2. False

Q.

For what value of a and b, the algebraic expression a³ + b³ - 3ab(a + b) equals 37.

1. a = -1; b = 1

2. a = 2; b = -3

3. a = -2; b = 3

4. a = 1; b = -2

Q. Write the algebraic expression 4x + 8 in words.

1. 4 more than 4 times a number x
   
2. 4 less than 8 times a number x
3. 8 more than 4 times a number x
4. 8 less than 4 times a number x

Q. Find the degree of the following expression:
$x^5{y}^7-8x^3{y}^8+10x^4{y}^5{z}^4$.

1. 12
2. 11
3. 13
4. 10

Q. What is the coefficient of $y$ in the term $-13xy$?

1. 13
2. -13
3. $13x$
4. $-13x$

Q. Choose the correct option for the given equation.
$(a+b{)}^2=a^2+2ab+b^2$

1. The equation is true for all the values of a and b.
2. The equation is true for all the values of a but only few values of b.
3. The equation is true for all the values of b but only few values of a.
4. The equation is not true for all the values of a and b.

Q. All equations are identities but all identities may not be equations.

1. True
2. False

Q. 28. What is difference between equations and identities?

Q.

Classify the following polynomials as monomial, binomial and trinomial polynomials:

$x^2-5$

Q. What is the sum of the coefficients of $x^2$ in the polynomials

$p\left(x\right)=x^2+2x+1$
$q\left(x\right)=3x^2+4x+2$ ?

1. 3
2. 4
3. 5
4. 6

Q.

How to add and substract algebraic expression

Q. Find the value of ${\left(106\right)}^3-{\left(94\right)}^3$

Q. The algebraic expression $6x^2-24xy+19$ is a .

1. Monomial
2. Binomial
3. Trinomial

Q.

$2x^2+3xy+4x{y}^2+5z$ is an algebraic expression.

1. True
2. False

Q. 5 is added to three times the product of numbers m and n.
Express the above statement as an algebraic expression.

1. $5(mn+3)$
2. $(3m+n+5)$
3. $(3mn+5)$
4. $3(mn+5)$

Q. What is the rule to find the number of non-square numbers between two consecutive perfect squares?

Q. Like terms are terms that contain the same variable with the same .

1. Coefficient
2. Exponent
3. constant

Q. If the product of four consecutive natural numbers increased by a natural number $\rho$ is a perfect square, then the value of $\rho$ is:

1. 2
2. 8
3. 4
4. 1

Q. How many numbers lie between squares of the following numbers?

12 and 13

Q.

Coefficient of $x{y}^2$ in the term -$\frac{4x{y}^2}{9}$ is:

1. -3
   

2. ​

3. -​

4. -1
   

Q.

I want learn division of algebraic expressions but there are no videos regarding the topic

Q. Which expression is a factor of $m^4-16$?

1. $m+5$
2. $m-4$
3. $m^2+2$
4. $m-2$

Q. Choose the correct option based on the given statements.

Statement 1:- All identities are equations.
Statement 2:- All equations are identities.

1. Statement 1 is true but statement 2 is false.
2. Statement 2 is true but statement 1 is false.
3. Both the statements are true.
4. Both the statements are false.

Q.

An algebraic expression obtained by multiplying x² with 12 and subtracting 5 from it is ______ .

1. -7x²

2. 5 - 12x²

3. 12x² - 5

4. 7x²