Algebraic expressions are made from variables and constants in conjunction with mathematical operators. These expressions don't have any facets or signals like algebraic equations. Example – 4x²+3x-6, 7x+1, etc.
Some basic terminology :
- Factors - This means all the possible parts of the product. One is a basic factor for everything. Example- factors of 7x are 1,7,x, and 7x.
- Terms - A variable or constant, or a constant multiplied by a variable, is Known as a term. Example -4y, 7, 9x.
- Coefficients - Formation of the term when a constant is multiplied by variable/variables; that constant is Known as coefficients. Example – 6x, here 6 is the coefficient.
Some basic terminology :
There are three types of expressions in Algebra:
- Monomial Expression - An expression that includes only one term is Known as Monomial Expression. For example - 10x, 6y.
- Binomial Expression - An expression with two different or unlike terms is known as Binomial Expression. For example- 70xy+10
- Polynomial Expression - An expression that consists of more than one term with non-negative integer exponents is known as Polynomial Expression. For example – 4x+6y+8z.
Algebraic Identities
When equality holds true for all then it is understood as Identities. There are 4 Identities:
(x+y)² = x²+y²+2xy
(x-y)² = x²+y²-2xy
(x+y)(x-y) = x²-y²
(x+y+z)² = x²+y²+z²+2xy+2yz+2zx
Algebraic Expressions and Identities Sample Questions for Class 8
Question 1
can be expressed as ______.
A. 0
B. a + b + c
C. 1
D. –(a + b + c)
Question 2
The value of 3 – 3 + 3 is _______.
A. –247500
B. 251750
C. 125320
D. 12345
Question 3
The value of (x + 3)3 – (x – 3)3 is _____.
A. 0
B. 1 – x3
C. 3x2 – 5
D. 18x2 + 54
Question 4
If then
A.
B. 9
C.
D. 8
Question 5
What must be added to x3 + 3x – 8 to get 3x3 + x2 + 6?
A. 2x3 + x2 – 3x + 14
B. 2x3 + x2 + 14
C. 2x3 + x2 – 6x – 14
D. x3 + x2 + 14