Factorize k2 – 81
a) k2 – 92 +18k
b) (k – 9)(k – 9)
c) (k – 9)(k + 9)
Solution:we know that a2–b2=(a+b)(a–b)
(a + b)3=……………….
a) a3 + 3ab2 + 3ab2 + b3
b)a3 + 3ab(a+b) 2+b3
c)a2 + b2 + 3a2b + 3ab2
d)a3 + 3a2b + 3ab2 + b3
Solution: We know that
(a+b)3= a3 + 3a2b + 3ab2 + b3Or
(a+b)3= a3 + 3ab(a+b) + b3
Cube of 2x – 7y is………..
a) 8x3 – 84x2y + 294xy2 – 343y3
b)8x2 – 42x2y + 294x2y – 343y2
c)4x2+42x2y + 294 x2y + 343y3
d)4x3+84x2y + 294 x2y + 343y2
Solution: Solve according to the formula
(a – b)3= a3– 3a2b + 3ab2– b3
Find a3 – b3 if a – b =6 and ab=3
a) 216
b) 270
c) 648
d) 712
Solution: a – b = 6 (a – b)3 = (6)3
(a)3 – 3(a)2(b) + 3(a) (b)2 – (b)3 = 216
a3 – 3ab(a – b) – b3 = 216 put values
a3–3×3(6)–b3=216 a3–54–b3=216
a3– b3= 216+54 a3– b3=270
Solution of the equation 2x+5=8
a) 2/3
b) 3/2
c) 2/4
d) 4/2
Solution: 2x+5=8 2x= 8 – 5
2x = 3 x= 3/2
(50)2 – (19)2= ………….
a) 361
b) 961
c) 2139
d) 2861
Solution:(50)2 – (19)2 = (50×50)–(19×19)
2500 – 361 = 2139
