Algebraic Expressions And Identities- 1 - Free MCQ Practice Test with solutions,

A binomial expression consists of exactly two terms connected by addition or subtraction.

• Option D, 4x + 7, has two distinct terms: 4x and 7, making it a binomial.
• The other options (A, B, C) are monomials as they contain only one term each.

2x + 7

A binomial is a mathematical expression consisting of two terms. In this case, 2x + 7 is a binomial because it has two terms: 2x and 7.

• 7 – 3x + 4 is not a binomial because it has three terms: 7, -3x, and 4
• 4x + y + 2 is not a binomial because it has three terms: 4x, y, and 2
• 3x is not a binomial because it has only one term: 3x

Writing the three expressions in separate rows, with like terms one below the other, we have

7xy + 5yz    – 3zx

+        4yz   + 9zx        – 4y

+ –2xy        – 3zx  + 5x         

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= 5xy + 9yz + 3zx  + 5x – 4y

Thus, the sum of the expressions is 5xy + 9yz + 3zx + 5x – 4y. Note how the terms, – 4y

in the second expression and 5x in the third expression, are carried over as they are, since

they have no like terms in the other expressions.

- A monomial is an algebraic expression containing only one term.
- It can be a constant, a variable, or a product of constants and variables.
- For example, 7, and -3xy are all monomials.
- A binomial has two terms, and a trinomial has three.
- Therefore, the correct answer is A: monomial, as it describes an expression with a singular term.

(xy+yz)²-(xy-yz)²

xy² +yz² +2.xy.yz -(xy²+yz²-2xy.yz)

(xy)² +(yz)² +2xy²z -[(xy)² +(yz)² -2xy²z

(xy)² +(yz)² +2xy²z -(xy²)-(yz)² + 2xy²z


Cancelled (xy)² +(yz)² and -(xy²)-(yz)².

2xy²z+ 2xy²z

=> 4xy²z


Hence, Value of (xy + yz)² – (xy – yz)² => 4xy²z


Note;-

(a+b)²-(a-b)² = 4ab

(xy + yz)² - 2x²y²z
Substitute values

= ((-1)(1) + (1)(2))² - 2(-1)²(1)²(2)

= (-1 + 2)² - 4

= 1 - 4

= -3

x² - a² = ( x + a) (x - a) using this equation.

5² - 4² = ( 5 + 4) ( 5 - 4 )= ( 9 ) (1 )= 9 

To find: 6² - 5²:

Putting x = 6 and a = 5 in identity x² - a² = (x - a)(x+a);

⇒ 6²- 5² = (6 - 5)(6 + 5) = 11.

• Terms consist of variables, constants, and coefficients.
• Adding these terms combines their values and components.
• The combination results in a mathematical expression.
• Therefore, terms are added to form expressions.