Question

BT: Tính thuận tiện:

a, 49 . 51

b, 29 . 31

c, 101²

d, 99² + 2.99 +1

e, ( 10² + 8² + 6² + 4² + 2² ) - ( 9² + 7² + 5² + 3² + 1² )

f, 1998² - 1997. ( 1998 + 1 )

Answer 1

a) \(49.51=\left(50-1\right)\left(50+1\right)=50^2-1^2=2500-1=2499\)

b) \(29.31=\left(30-1\right)\left(30+1\right)=30^2-1^2=900-1=899\)

c) \(101^2=\left(100+1\right)^2=100^2+2.100.1+1^2=10000+200+1=10201\)

d) \(99^2+2.99+1=\left(99+1\right)^2=100^2=10000\)

e) \(\left(10^2+8^2+6^2+4^2+2^2\right)-\left(9^2+7^2+5^2+3^2+1^2\right)\)

\(=10^2-9^2+8^2-7^2+6^2-5^2+4^2-3^2+2^2-1^2\)

\(=\left(10-9\right)\left(10+9\right)+\left(8-7\right)\left(8+7\right)+\left(6-5\right)\left(6+5\right)+\)

\(\left(4-3\right)\left(4+3\right)+\left(2-1\right)\left(2+1\right)\)

\(=10+9+8+7+6+5+4+3+2+1=55\)

f) \(1998^2-1997.\left(1998+1\right)=1998^2-\left(1998-1\right)\left(1998+1\right)\)

\(=1998^2-1998^2+1=1\)