Question -
Answer -
(i) a2 + 8a + 16
Here, 4 + 4 = 8 and 4 × 4 = 16
a2 + 8a +16
= a2 + 4a + 4a + 4× 4
= (a2 + 4a) + (4a +16)
= a(a + 4) + 4(a + 4)
= (a + 4) (a + 4)
= (a + 4)2
(ii) p2 – 10p + 25
Here, 5 + 5 = 10 and 5 × 5 = 25
p2 – 10p + 25
= p2 – 5p – 5p + 5× 5
= (p2 – 5p) + (-5p +25)
= p(p – 5) – 5(p – 5)
= (p – 5) (p – 5)
= (p – 5)2
(iii) 25m2 + 30m + 9
Here, 15 + 15 = 30 and 15 × 15 = 25 × 9 = 225
25m2 + 30m + 9
= 25m2 + 15m + 15m + 9
= (25m2 + 15m) + (15m+ 9)
= 5m(5m + 3) + 3(5m + 3)
= (5m + 3) (5m + 3)
= (5m + 3)2
(iv) 49y2 + 84yz + 36z2
Here, 42 + 42 = 84 and 42 × 42 = 49 × 36 = 1764
49y2 + 84yz + 36z2
= 49y2 + 42yz + 42yz+ 36z2
= 7y(7y + 6z) +6z(7y + 6z)
= (7y + 6z) (7y + 6z)
= (7y + 6z)2
(v) 4x2 – 8x + 4
= 4(x2 – 2x + 1)[Taking 4 common]
= 4(x2 – x – x + 1)
= 4[x(x – 1) -1(x – 1)]
= 4(x – 1)(x – 1)
= 4(x – 1)2
(vi) 121b2 – 88bc + 16c2
Here, 44 + 44 = 88 and 44 × 44 = 121 × 16 = 1936
121b2 – 88bc + 16c2
= 121b2 – 44bc – 44bc+ 16c2
= 11b(11b – 4c) – 4c(11b – 4c)
= (11b – 4c) (11b – 4c)
= (11b – 4c)2
(vii) (l + m)2 – 4lm
Expanding (l + m)2, we get
l2 + 2lm + m2 – 4lm
= l2 – 2lm + m2
= l2 – Im – lm + m2
= l(l – m) – m(l – m)
= (l – m) (l – m)
= (l – m)2
(viii) a4 + 2a2b2 + b4
= a4 + a2b2 + a2b2 + b4
= a2(a2 + b2) + b2(a2 + b2)
= (a2 + b2)(a2 + b2)
= (a2 + b2)2