Types of Expressions Based on the Number of Terms

Q.

If $a+b+c=0$, then prove that $a^3+b^3+c^3=3abc$.

Q.

Give one example of a monomial of degree $100$.

Q. Which of the following algebraic expressions is a trinomial?

1. 3xyz
2. 3x + 2y + 5x
3. 7x - 3y + 0
4. 5a + 3b + 10

Q.

Classify the following algebraic expressions as monomials, binomials, trinomials or polynomials.

(i) $7x$ (ii) $5y-7z$ (iii) $3x^3-5x^2-11$ (iv) $1-8a-7a^2-7a^3$

(v) $5m-3$ (vi) $a$ (vii) $4$

(viii) $3y^2-7y+5$

Q.

Fill in the blanks to make the statement true.

Number of terms in a monomial is ___.

Q.

Question 49

State whether the statement given is True or False.

If we add a monomial and binomial, then answer can never be a monomial.

Q. Which of the following algebraic expressions is a trinomial?

1. 2x + 6 + 3x
2. 5y + 15xy + 6x
3. 9x + 2y - 6xy - 9x
4. 7y + 21z - 9x + 6xy

Q.

A polynomial of degree $5$ in $x$ has at most.

1. $5$ term

2. $4$ term

3. $6$ term

4. $10$ term

Q.

Question 34

State whether the statement given is True or False.

(3a - b + 3) - (a + b) is a binomial.

Q.

Question 53 (j)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Quotient of x and 15 multiplied by x.

Q.

Question 53 (l)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Two times q subtracted from cube of q.

Q.

Question 35

State whether the statement given is True or False.

A trinomial can be a polynomial.

Q.

Question 36

State whether the statement given is True or False.

A polynomial with more than two terms is a trinomial.

Q.

A binomial has more than two terms. State whether the statement given is True or False.

1. True
2. False

Q.

$1.$ Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials.

Include common errors to watch out for when using each of these methods.

$2.$ Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.
As an added challenge, develop a model similar to algebra tiles that will allow you to show this multiplication.

Describe an example of your model for the product $\left(x+1\right)\left(x^2+2x+2\right)$.
$3.$ Imagine that you are teaching a new student how to multiply polynomials.

Explain how multiplying polynomials is similar to multiplying integers.

Then describe the key differences between the two.
$4.$ If you multiply a binomial by a binomial, how many terms are in the product (before combining like terms)?

What about multiplying a monomial by a trinomial? Two trinomials?
Write a statement about how many terms you will get when you multiply a polynomial with $m$ terms by a polynomial with $n$ terms.

Give an explanation to support your statement.

Q.

Question 30

Fill in the blanks to make the statement true.

On adding a monomial ___ to $-2x+4y^2+z,$ the resulting expression becomes a binomial.

Q.

Question 50

State whether the statement given is True or False.

If we subtract a monomial from a binomial, then answer is at least a binomial.

Q.

The coefficient of x in '2x +5y' is __

Q.

Find the value of : $\frac{x^{a(b-c)}}{x^{b(a-c)}}÷(\frac{x^b}{x^a}{)}^c$

1. a

2. b

3. 1

4. 0

Q.

Question 53 (e)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Perimeter of an equilateral triangle of side x.

Q.

Question 53 (a)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

x is multiplied by itself and then added to the product of x and y.

Q.

Question 53 (c)

Write the following statements in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Product of p, twice of q and thrice of r.

Q.

Question 42

State whether the statement given is True or False.

The expression x + y + 5x is a trinomial.

Q.

Question 40

State whether the statement given is True or False.

A trinomial has exactly three terms.

Q.

Question 51

State whether the statement given is True or False.

When we subtract a monomial from a trinomial, then answer can be a polynomial.

Q.

Question 39

State whether the statement given is True or False.

A binomial has more than two terms.

Q.

Question 53 (f)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Perimeter of a rectangle with length p and breadth q.

Q.

Question 53 (b)

Write the following statement in the form of algebraic expressions and write whether is monomial, binomial or trinomial.

Three times of p and two times of q are multiplied and then subtracted from r.

Q. An algebraic expression consisting of three terms is called a ______ expression.

1. monomial
2. trinomial
3. binomial
4. polynomial

Q.

Question 52

State whether the statement given is True or False.

When we add a monomial and a trinomial, then answer can be a monomial.