\(99^3+1+3\left(99^2+99\right)\)

\(=99^3+3.99^2.1+3.99.1^2+1^3\)

\(=\left(99+1\right)^3\)

\(=100^3\)

\(=1000000\)

\(99^3+1+3\left(99^2+99\right)=99^3+1^3+3.99^2+3.99=99^3+3.99^2.1+3.99.1^2+1^3=\left(99+1\right)^3=100^3=1000000\)

\(x^2-x+1=x^2-2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2+\frac{3}{4}\)

\(=\left(x+\frac{1}{2}\right)+\frac{3}{4}\ge\frac{3}{4}>0\)( đpcm )

\(2004^2-16\)

\(=\left(2004-4\right)\left(2004+4\right)\)

\(=2000.2008\)

\(=4016000\)

\(99^3+1+3\left(99^2+99\right)=99^3+3.1.99^2+3.1^2.99+1^3=\left(99+1\right)^3=100^3=1000000.\)

a)\(36^2+26^2-52.36\)

=\(\left(36-26\right)^2\)

=\(10^2\)

=100

b)\(99^3+1+3\cdot\left(99^2+99\right)\)

\(=99^3+\left(3\cdot99^2\cdot1\right)+\left(3\cdot99\cdot1^2\right)+1^3\)

\(=\left(99+1\right)^3=100^3=100000\)

b) 37,5 . 6,5 – 7,5 . 3,4 – 6,6 . 7,5 + 3,5 . 37,5 = (37,5 . 6,5 + 3,5 . 37,5) - (7,5 . 3,4 + 6,6 . 7,5) = 37,5(6,5 + 3,5) - 7,5(3,4 + 6,6) = 37,5 . 10 - 7,5 . 10 = 375 - 75 = 300. 

a) 45^2 + 40^2 – 15^2 + 80 . 45 = 45^2 +2 . 40 . 45 + 40^2 – 15^2 = (40 + 45)^2 – 15^2 = 852 – 152 = (85 – 15)(85 + 15) = 70 . 100 = 7000.

đó là HĐT số 6

(A+B)^3=A^3+3A^2B+3AB^2+B^3 

99^3+1+3(99^2+99)=99^3+3*99^2*1+3*99*1^2+1^3=(99+1)^3=1000000

=(99+1)^3=100^3=1000000

 \(M=1995^2-1994.1996\)       

     \(=1995^2-\left(1995-1\right)\left(1995+1\right)\)

     \(=1995^2-\left(1995^2-1\right)=1\)

\(N=9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)\)

   \(=18^8-\left(18^8-1\right)=1\)

\(K=99^3+3.99^2+3.99+1\)

   \(=99^3+3.99^2.1+3.99.1^2+1^3\)

   \(=\left(99+1\right)^3\)

   \(=100^3=1000000\)

Chúc bạn học tốt.

Bài làm:

c) \(M=1995^2-1994.1996=1995^2-\left(1995-1\right)\left(19995+1\right)=1995^2-1995^2+1^2=1\)

d) \(N=9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)=18^8-18^8+1^2=1\)

e) \(K=99^3+3.99^2+3.99+1=\left(99+1\right)^3=100^3=1000000\)

Học tốt!!!!!