Algebraic Expressions and Identities Test - 1

Explanation:

As this expression has number, symbol and operators grouped together.

Explanation:

An algebraic expression consisting of unlike terms is called a binomial. 

so, 2x+7 is a binomial as it contains two unlike terms i.e 2x and 7.

Explanation:

(xy + yz)²− (xy − yz)²

Using identity x² - a² = (x + a) (x - a)

= [(xy + yz) + (xy - yz)] [(xy + yz) - (xy - yz)]

= (xy + yz + xy - yz) (xy + yz - xy + yz)

= (2xy) (2yz) = 4xy²z

Explanation:

Monomial is a type of algebraic expression which contains only one term. So,  Expression that contains only one term is called a monomial. 

Explanation:

here x = 6 and a = 5

Put in the identity, (x−a)(x+a)=x²−a²

6² - 5² = (6 - 5) (6 + 5) = (1) (11) = 11 

Explanation:

Terms separated with mathematical operation like + or - forms expression. So terms are added to form expression.

Explanation:

(7xy + 5yz – 3zx) + (4yz + 9zx – 4y) + (–3xz + 5x – 2xy)

= 7xy + 5yz – 3zx + 4yz + 9zx – 4y – 3xz + 5x – 2xy

= 7xy – 2xy + 5yz + 4yz – 3zx + 9zx – 3xz + 5x – 4y

= 5xy + 9yz + 3zx + 5x – 4y

Explanation:

To find 5² - 4² with identity x² - a² = (x - a) (x + a), here x = 5 and a = 4

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

Explanation:

Simplify(xy + yz)²− 2x²y²z.  Find the value when x = -1, y = 1 and z = 2.

Putting the values in expression,

[(-1)(1) + (1)(2)]² - 2(-1)²(1)²(2)

= [-1 +2]² - 2 (1) (1) (2)

= (1)² - 4 = 1 - 4 = -3

Explanation:

As it has the same variables.