Algebraic Expressions Class 7 Notes Maths Chapter 10

Students can go through AP 7th Class Maths Notes Chapter 10 Algebraic Expressions to understand and remember the concepts easily.

Class 7 Maths Chapter 10 Notes Algebraic Expressions

→ There are four fundamental operations likely addition (+), subtraction (-), multiplication (×) and division (÷).

→ We use lower case letters like a, b, c, x, y, z etc., to denoted a variable.

→ Expressions like y + \(\frac{3}{2}\), 7x – 3, 6 – p, etc., are the examples of simple algebraic expressions.

→ A variable can take various values, its values is not fixed.

→ A constant has a fixed value.
Ex : 7, 100, -20, 2024

→ We combine variables and constants to make algebraic expressions.

→ While forming algebraic expressions we use the operations such as +, -, ×, ÷
Ex : 7p + 4, 1 – p, 3 × p, p ÷ 6.

→ y², 2p², 3y² – 7, 9xy – \(\frac{3}{2}\), …., etc., are some examples of expressions.

→ x × x = x², can be read as x squared.

→ p × p × p = p³, can be read as p cubed.

→ y, y², y³, ………. are all algebraic expressions obtained from y.

→ In 2x + 11, 2x and 11 are called the terms.

→ Parts of an expression which are formed separately first and then added are known as terms.

→ Terms are added to form expressions.
Ex : – 3xy + 2 + y.

→ In 5x²y + 7x + 1,
5x²y = 5 × x × x × y
here 5, x and y are called factors of 5x²y
7x = 7 × x
here 7 and x are the factors of 7x.

→ A term is a product of its factors.

→ Tree Diagram :

→ ‘1’ is a factor of every term.

→ Coefficient: The numerical factors is said to be the numerical coefficient (or) simply the coefficient of the term.
Ex:

1. The coefficient of x in 5x is 5.
2. The coefficient of pq in 7pq + 1 is 7.

→ Like and Unlike terms : When terms having same algebraic factors, they are like terms.
Ex: 7xy, -6xy, \(\frac{1}{2}\)xy, …………. etc.
When terms having different algebraic factors, they are unlike terms.
Ex : 9ab, 7pqr, xy, ……….. etc.

→ Monomial : An expression with only one term is called a Monomial.
Ex : 7p, \(\frac{9}{2}\)p²q, 3xy, 7r, …………. etc.

→ Bionomial : An expression with only two terms is called a Binomial.
Ex : p + q², 9 – z, \(\frac{x y}{2}\) + 3, \(\frac{7}{2}\) – x, etc.

→ Trionomial : An expression contains three terms is called Trinomial.
Ex : x + \(\frac{y}{2}\) – 3, p – q + r, \(\frac{x y}{2}\) + 3 + 9l.

→ Polynomial : An expression with one or more terms is called a polynomial.
Ex : 7p, 9xy + 1, p + q + \(\frac{r}{2}\)
9xy – \(\frac{3 x}{2}\) + 7r – 1

→ Every monomial, binomial and trinomial are all polynomials.

→ The value of an expressions : In an expression when a variable (or) variables is given a particular value we can find the value of that expression.
Ex : 1) Find the value of 7 – x² + x at x = 0.
Solution:
7 – x² + x
At x = 0
Value of the expression = 7 – (0)² + 0
= 7 – 0 + 0 = 7

2) Find the value of the expression
9xy – x – y + 4 at x = 1, y = 2
Solution:
x = 1, y = 2
9xy – x – y + 4
= 9(1)(2) – 1 – 2 + 4
= 18 – 3 + 4
= 22 – 3 = 19.
∴ The value of above expression is 19.

→ Some formulae:
i) (a + b)² = a² + 2ab + b²
ii) (a – b)² = a² – 2ab + b²
iii) a² – b² = (a + b) (a – b)
iv) (a – b)³ = a³ – 3a²b + 3ab² – b³
v) (a – b)³ = a³ – 3ab(a – b) – b²
vi) (a + b)³ = a³ + 3a²b + 3ab² + b³
vii) (a + b)³ = a³ + 3ab(a + b) + b³
viii) (a – b)² + 4ab = (a + b)²
ix) (a – b)² – (a – b)² = 0
x) (a + b)² – 4ab = (a – b)²