. Factorize the expressions:
(i) 4a^2
- 12ab + 9b^2 (ii) 36p^2
- 84pq + 49q^2 (iii) 4a^8
- b^8
(iv) (z - 1)^2+ 2 (z-1) (2z+3) + (2z +3)^2
Answers
Answer:
We have to make use of following identities to factorize them
(a+b)2= a2 +b2 +2 ab
(a-b)2= a2 +b2 -2 ab
a2 –b2 = (a-b)(a+b)
1) a² + 8a + 16
= a2 + 2×a× 4 + 42
So from first identity, it can be written as
=(a+4)2
2) p² – 10 p + 25
= p2 - 2×p× 5 + 52
So from second identity, it can be written as
=(p-5)2
3) 25m² + 30m + 9
= (5m)2 + 2×5m× 3 + 32
So from first identity, it can be written as
=(5m+3)2
4) 49y² + 84yz + 36z²
= (7y)2 + 2×7y× 6z + (6z)2
So from first identity, it can be written as
=(7y+6z)2
5) 4x² – 8x + 4
= (2x)2 - 2×2x× 2 + 22
So from second identity, it can be written as
=(2x-2)2
= 4(x-1)2 taking common factor 2 out of square
6) 121b² – 88bc + 16c²
= (11b)2 - 2×11b× 4c + (4c)2
So from second identity, it can be written as
=(11b-4c)2
7) (l + m) ² – 4lm
=l2 + m2 +2lm -4lm
= l2 + m2 -2lm
So from second identity, it can be written as
=(l-m)2
8) a4 + 2a²b² + b4
= (a2)2 + 2a²b²+(b2)2
So from first identity, it can be written as
=(a²+b²)²