ex 9.5 q4 Class 8 Algebraic Expressions and Identities - NCERT - Maths Class 8th chapter 9 SIMPLIFY

ex 9.5 q4 Class 8 Algebraic Expressions and Identities - NCERT - Maths Class 8th - chapter 9
EXERCISE 9.5
1. Use a suitable identity to get each of the following products. (i) (x + 3) (x + 3) (ii) (2y + 5) (2y + 5) (iii) (2a – 7) (2a – 7) (iv) (3a – 1 2 ) (3a – 1 2 ) (v) (1.1m – 0.4) (1.1m + 0.4) (vi) (a2 + b2 ) (– a2 + b2 ) (vii) (6x – 7) (6x + 7) (viii) (– a + c) (– a + c) (x) (7a – 9b) (7a – 9b)
2. Use the identity (x + a) (x + b) = x2 + (a + b) x + ab to find the following products. (i) (x + 3) (x + 7) (ii) (4x + 5) (4x + 1) (iii) (4x – 5) (4x – 1) (iv) (4x + 5) (4x – 1) (v) (2x + 5y) (2x + 3y) (vi) (2a2 + 9) (2a2 + 5) (vii) (xyz – 4) (xyz – 2)
3. Find the following squares by using the identities. (i) (b – 7)2 (ii) (xy + 3z)2 (iii) (6x2 – 5y) (v) (0.4p – 0.5q)2 (vi) (2xy + 5y)2
4. Simplify. (i) (a2 – b2 ) 2 (ii) (2x + 5)2 – (2x – 5)2 (iii) (7m – 8n) 2 + (7m + 8n)2 (iv) (4m + 5n) 2 + (5m + 4n)2 (v) (2.5p – 1.5q)2 – (1.5p – 2.5q)2 (vi) (ab + bc)2 – 2ab2 c (vii) (m2 – n2 m)2 + 2m3 n2
5. Show that. (i) (3x + 7)2 – 84x = (3x – 7)2 (ii) (9p – 5q) 2 + 180pq = (9p + 5q) (iv) (4pq + 3q)2 – (4pq – 3q) 2 = 48pq2 (v) (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0
6. Using identities, evaluate. (i) 712 (ii) 992 (iii) 1022 (iv) 9982 (v) 5.22 (vi) 297 × 303 (vii) 78 × 82 (viii) 8.92 (ix) 1.05 × 9.5
7. Using a2 – b2 = (a + b) (a – b), find (i) 512 – 492 (ii) (1.02)2 – (0.98)2 (iii) 1532 – 1472 (iv) 12.12 – 7.92
8. Using (x + a) (x + b) = x2 + (a + b) x + ab, find (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8

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.