Скачать или смотреть ex 9.2 q3, 4, 5 class 8 Algebraic Expressions and Identities - NCERT Class 8th Maths - chapter 9

ex 9.2 q3, 4, 5 class 8 Algebraic Expressions and Identities - NCERT Class 8th Maths - chapter 9
Algebraic Expressions and Identities
Algebraic Expressions
Algebraic expressions are the mathematical statement that we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

What are Algebraic Expressions?
An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc. 5x + 7 is an example of an algebraic expression. Here are more examples:
5x + 4y + 10
2x2y - 3xy2
(-a + 4b)2 + 6ab

Variables, Constants, Terms, and Coefficients
There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.
In mathematics,
• a symbol that doesn't have a fixed value is called a variable. Some examples of variables in Math are a,b, x, y, z, m, etc.
• On the other hand, a symbol that has a fixed numerical value is called a constant. All numbers are constants. Some examples of constants are 3, 6, -(1/2), √5, etc.
• A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants by the operation of multiplication or division. Some examples of terms are 3x2, -(2y/3), √(5x), etc.
• Here, the numbers that are multiplying the variables are 3, -2/3, and 5. These numbers are called coefficients.
What are Expressions? - Terms, Factors and Coefficients - Monomials, Binomials and Polynomials
Like and Unlike Terms
EXERCISE 9.1 we identify terms and classify expression as monomials or binomials or trinomials or polynomials. In this exercise we identify like and unlike terms to add or subtract them.
1. Identify the terms, their coefficients for each of the following expressions. (i) 5xyz2 – 3zy (ii) 1 + x + x2 (iii) 4x2 y2 – 4x2 y2 z2 + z2 (iv) 3 – pq + qr – rp (v) 2 2 x y + − xy (vi) 0.3a – 0.6ab + 0.5b
2. Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? x + y, 1000, x + x2 + x3 + x4 , 7 + y + 5x, 2y – 3y2 , 2y – 3y2 + 4y3 , 5x – 4y + 3xy, 4z – 15z2 , ab + bc + cd + da, pqr, p2 q + pq2 , 2p + 2q
3. Add the following. (i) ab – bc, bc – ca, ca – ab (ii) a – b + ab, b – c + bc, c – a + ac (iii) 2p2 q2 – 3pq + 4, 5 + 7pq – 3p2 q2 (iv) l 2 + m2 , m2 + n2 , n2 + l 2 , 2lm + 2mn + 2nl
4. (a) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3 (b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz (c) Subtract 4p2 q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q + 5pq – 2pq2 + 5p2 q

Multiplication of Algebraic Expressions: Introduction - Multiplying a Monomial by a Monomial - Multiplying three or more monomials –
EXERCISE 9.2 in this exercise we learn to find product of monomials, binomials, and areas of rectangles with pairs of monomials as their lengths and breadths. In other question we obtain the volume of rectangular boxes with the following length, breadth and height.
1. Find the product of the following pairs of monomials. (i) 4, 7p (ii) – 4p, 7p (iii) – 4p, 7pq (iv) 4p3 , – 3p (v) 4p, 0
2. Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively. (p, q); (10m, 5n); (20x2 , 5y2 ); (4x, 3x2 ); (3mn, 4np)
4. Obtain the volume of rectangular boxes with the following length, breadth and height respectively. (i) 5a, 3a2 , 7a4 (ii) 2p, 4q, 8r (iii) xy, 2x2 y, 2xy2 (iv) a, 2b, 3c
5. Obtain the product of (i) xy, yz, zx (ii) a, – a2 , a3 (iii) 2, 4y, 8y2 , 16y3 (iv) a, 2b, 3c, 6abc (v) m, – mn, mnp

Multiplying a monomial by a binomial - Multiplying a monomial by a trinomial
EXERCISE 9.3 In this exercise we carried out multiplication of the expressions, we hs to find the product of expressions and we simplified some problems with given value for variable. We added and subtracted certain expressions also.
1. Carry out the multiplication of the expressions in each of the following pairs. (i) 4p, q + r (ii) ab, a – b (iii) a + b, 7a2 b2 (iv) a2 – 9, 4a (v) pq + qr + rp, 0
3. Find the product. (i) (a2 ) × (2a22) × (4a26) (iv) x × x2 × x3 × x4
4. (a) Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x = 1 2 . (b) Simplify a (a2 + a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 (iii) a = – 1.
5. (a) Add: p ( p – q), q ( q – r) and r ( r – p) (b) Add: 2x (z – x – y) and 2y (z – y – x) (c) Subtract: 3l (l – 4 m + 5 n) from 4l ( 10 n – 3 m + 2 l ) (d) Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c )