Algebraic expressions are formed from variables and constants.
This is followed by the topics terms, factors, and coefficients.
Expressions are made up of terms.
A term is a product of factors.
Coefficient is the numerical factor in the term
Before moving to terms like monomials, binomials, and polynomials, like and unlike terms are discussed.
When terms have the same algebraic factors, they are like terms.
When terms have different algebraic factors, they are unlike terms.
Any expression with one or more terms is called a polynomial.
A one-term expression is called a monomial.
A two-term expression is called binomial.
An expression that contains three terms is called a trinomial.
Emphasis is given to important topics like the Addition and Subtraction of Algebraic Expressions.
2 sub parts are discussed in the following section:
Adding and subtracting like terms: The sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.
The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
Adding and subtracting general algebraic expressions
The like terms are added together while the unlike terms are left as they are.
The next part of the section explains about Finding the Value of an Expression where value of a variable is given depending on which value of the expression is calculated.
This is followed by the topic- Using Algebraic Expressions- Formulas and Rules where one understands how algebraic expressions can be used to write formulas and patterns. These patterns are related to numbers and geometrical patterns.
Perimeter formulas
Area formulas
Rules for number patterns
Some more number patterns
Pattern in geometry
Unsolved, solved exercises, questions in different patterns will make the chapter more comprehensible to students.
All important points of the chapter are cited in the end under the title- What Have We Discussed?
Page No 234:
Question 1:
Get the algebraicexpressions in the following cases using variables, constants and arithmetic operations.
(i) Subtraction of z from y.
(ii) One-half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii)Sum of numbers a and b subtracted from their product.
ANSWER:
(i) y − z
(ii)
(iii) z2
(iv)
(v) x2 + y2
(vi) 5 + 3 (mn)
(vii) 10 − yz
(viii) ab − (a + b)
Page No 234:
Question 2:
(i) Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams.
(a) x − 3 (b) 1 + x + x2 (c) y − y3
(d) (e) − ab + 2b2 − 3a2
(ii) Identify terms and factors in the expressions given below:
Step-by-step explanation:
-4
will be the ans, okay?
Algebraic expressions are formed from variables and constants.
This is followed by the topics terms, factors, and coefficients.
Expressions are made up of terms.
A term is a product of factors.
Coefficient is the numerical factor in the term
Before moving to terms like monomials, binomials, and polynomials, like and unlike terms are discussed.
When terms have the same algebraic factors, they are like terms.
When terms have different algebraic factors, they are unlike terms.
Any expression with one or more terms is called a polynomial.
A one-term expression is called a monomial.
A two-term expression is called binomial.
An expression that contains three terms is called a trinomial.
Emphasis is given to important topics like the Addition and Subtraction of Algebraic Expressions.
2 sub parts are discussed in the following section:
Adding and subtracting like terms: The sum of two or more like terms is a like term with a numerical coefficient equal to the sum of the numerical coefficients of all the like terms.
The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
Adding and subtracting general algebraic expressions
The like terms are added together while the unlike terms are left as they are.
The next part of the section explains about Finding the Value of an Expression where value of a variable is given depending on which value of the expression is calculated.
This is followed by the topic- Using Algebraic Expressions- Formulas and Rules where one understands how algebraic expressions can be used to write formulas and patterns. These patterns are related to numbers and geometrical patterns.
Perimeter formulas
Area formulas
Rules for number patterns
Some more number patterns
Pattern in geometry
Unsolved, solved exercises, questions in different patterns will make the chapter more comprehensible to students.
All important points of the chapter are cited in the end under the title- What Have We Discussed?
Page No 234:
Question 1:
Get the algebraicexpressions in the following cases using variables, constants and arithmetic operations.
(i) Subtraction of z from y.
(ii) One-half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii)Sum of numbers a and b subtracted from their product.
ANSWER:
(i) y − z
(ii)
(iii) z2
(iv)
(v) x2 + y2
(vi) 5 + 3 (mn)
(vii) 10 − yz
(viii) ab − (a + b)
Page No 234:
Question 2:
(i) Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams.
(a) x − 3 (b) 1 + x + x2 (c) y − y3
(d) (e) − ab + 2b2 − 3a2
(ii) Identify terms and factors in the expressions given below:
(a) − 4x + 5 (b) − 4x + 5y (c) 5y + 3y2
(d) (e) pq + q
(f) 1.2 ab − 2.4 b + 3.6 a (g)
(h) 0.1p2 + 0.2 q2
ANSWER:
(i)
(a)
(b)
(c)
(d)
(e)
(ii)
Row
Expression
Terms
Factors
(a)
− 4x + 5
− 4x
5
− 4, x
5
(b)
− 4x + 5y
− 4x
5y
− 4, x
5, y
(c)
5y + 3y2
5y
3y2
5, y
3, y, y
(d)
xy + 2x2y2
xy
2x2y2
x, y
2, x, x, y, y
(e)
pq + q
pq
q
p, q
q
(f)
1.2ab − 2.4b + 3.6a
1.2ab
− 2.4b
3.6a
1.2, a, b
− 2.4, b
3.6, a
(g)
thanku have a great day
(h)
0.1p2 + 0.2q2