Bài 1 :

\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)

\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)

\(\Rightarrow M< N\)

Bài 3 :

a) \(t^2+5t-8\) khi \(t=2\)

\(=5^2+2.5-8\)

\(=25+10-8\)

\(=27\)

b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)

\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)

\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)

c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)

\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)

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

Bài 2 :

a) \(...=2^3\left(19-14\right)+1=8.5+1=41\)

b) \(...=100-\left[60:\left(5^2-15\right)\right]=100-\left[60:10\right]=100-6=94\)

c) \(...=160:\left[17+\left(9.5-\left(14+2^3\right)\right)\right]=160:\left[17+\left(45-22\right)\right]=160:\left[17+23\right]=160:40=4\)

d) \(...=798+100\left[16-2\left(25-22\right)\right]=798+100\left[16-2.3\right]=798+100.10=798+1000=1798\)

a) Kết quả M = 0. Chú ý: nhân tử chung là 2f - 5 = 0.

b) Kết quả N = 300000.

c) Kết quả p = 0. Chú ý: nhân tử  x 2  + y -1 = 0.

d) Kết quả Q = 280. Chú ý: Q = (x - y)[ ( x   -   y ) 2  - xy].

a,

m x (n + p) = 4 x (5 + 3) = 4 x 8 = 32

(m + n) x p = (4 + 5) x 3 = 9 x 3 = 27

m x n + m x p = 4 x 5 + 4 x 3 = 20 + 12 = 32

m x p + n x p = 4 x 3 + 5 x 3 = 12 + 15 = 27

b,

- Hai biểu thức m x (n + p) và m x n + m x p có giá trị bằng nhau.

- Hai biểu thức (m + n) x p và m x p + n x p có giá trị bằng nhau.

Nếu m = 10, n = 5 , p = 2 thì

a) m + n + p = 10 + 5 + 2 = 17

m + ( n + p) = 10 + ( 5 + 2) = 17

b) m - n - p = 10 - 5 - 2 = 3

m - ( n + p )= 10 - (5 + 2) = 3

c) m + n x p = 10 + 5 x 2 = 20

(m + n) x p = ( 10 + 5 ) x 2 = 30

a) M = 2016.         b) N = 8100.          c) P = 2.

Nếu m = 10, n = 5 , p = 2 thì

m + n + p = 10 + 5 + 2 = 17

m + ( n + p) = 10 + ( 5 + 2) = 17

m - n - p = 10 - 5 - 2 = 3

m - ( n + p )= 10 - (5 + 2) = 3

m + n x p = 10 + 5 x 2 = 20

(m + n) x p = ( 10 + 5 ) x 2 = 30

a,10+5+2

=17

b,10+5-2

=13

c,10+5×2

=20

a = 17

b = 13

c = 30

a)ta co:m+n+p=10+5+2=17

b)ta co:m+n-p=10+5-2=13

c)ta co:m+n*p=10+5*2=10+10=20

a) \(M=\left(x+y\right)^3+2x^2+4xy+2y^2\)

\(=7^3+2\left(x^2+2xy+y^2\right)\)

\(=343+2\left(x+y\right)^2\)

\(=343+2.7^2\)

\(=343+98=441\)

b) \(N=\left(x-y\right)^3-x^2+2xy-y^2\)

\(=\left(-5\right)^3-\left(x-y\right)^2\)

\(=-125-\left(-5\right)^2\)

\(=-125-25=-150\)

\(a,M=\left(x+y\right)^3+2x^2+4xy+2y^2\)

\(=\left(x+y\right)^3+2\left(x^2+2xy+y^2\right)\)

\(=\left(x+y\right)^3+2\left(x+y\right)^2\)

\(=\left(x+y\right)^2\left(x+y+2\right)=7^2.9=49.9=441\)

\(b,N=\left(x-y\right)^3-x^2+2xy-y^2\)

\(=\left(x-y\right)^3-\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^3-\left(x-y\right)^2\)

\(=\left(x-y\right)^2.\left(x-y-1\right)\)

\(=\left(-5\right)^2\left(-5-1\right)=15.-6=-150\)

\(35\times m+35\times n+35\times p\)

\(=35\times\left(m+n+p\right)\)

Thay \(m=3;n=2;p=5\) vào biểu thức trên ta có:

\(35\times\left(3+2+5\right)=35\times10=350\)

35 x m + 35 x p + 35 x n

Thay số: ⇒ 35 x 3 + 35 x 5 + 35 x 2

= 35 x (3 + 5 + 2)

= 35 x 10

= 350