"Question 1 Factorise the following expressions. (i) a^2 + 8a + 16 (ii) p^2 − 10p + 25 (iii) 25m^2 + 30m + 9 (iv) 49y^2 + 84yz + 36z^2 (v) 4x^2 − 8x + 4 (vi) 121b^2 − 88bc + 16c^2 (vii) (l + m)^2 − 4lm (Hint: Expand (l + m)^2 first) (viii) a^4 + 2a^2b^2 + b^4
Class 8 Factorisation Page 223"
Answers
Factors:
In a product of two or more expressions each expression is called a factor of the product.
Factorization:
The process of writing a given expression as a product of two or more factors is called factorization.
Factorization when an expression is a complete square:
In this case we use the following formula
1. a²+2ab+b²= (a+b)²
2. a²-2ab+b²= (a-b)²
==========================================================
solution:
1) a² + 8a + 16
= a² + 2×a× 4 + 4²
[(a+b)²= a² +b² +2 ab]
=(a+4)²
2) p² – 10 p + 25
= p²- 2×p× 5 + 5²
(a-b)²= a² +b² -2 ab
=(p-5)²
3) 25m² + 30m + 9
= (5m)² + 2×5m× 3 + 3²
[(a+b)²= a² +b² +2ab]
=(5m+3)²
4) 49y² + 84yz + 36z²
= (7y)² + 2×7y× 6z + (6z)²
[(a+b)²= a² +b² +2 ab ]
=(7y+6z)²
5) 4x² – 8x + 4
= (2x)² - 2×2x× 2 + 2²
[(a-b)²= a² +b² -2 ab]
=(2x-2)²
= [2(x-1)² ] = 4(x-1) ²
6) 121b² – 88bc + 16c²
= (11b)² - 2×11b× 4c + (4c)²
[(a-b)²= a² +b² -2 ab]
=(11b-4c)²
7) (l + m) ² – 4lm
=l² + m² +2lm -4lm
= l² + m² -2lm
[a-b)²= a² +b² -2ab]
=(l-m)²
8) a⁴ + 2a²b² + b⁴
= (a²)² + 2a²b²+(b²)²
[(a+b)²= a² +b² +2 ab ]
=(a²+b²)²
=========================================================
Hope this help you...
Answer:
nikita singh her answers are correct