\(\text{A = (3 + 1) (3^2+ 1) (3^4 + 1) ... (3^{64} + 1)}\)Rút gọn biểu thức:
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8 tháng 3 2020

Ta có \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot\cdot\cdot\left(3^{64}+1\right)\)

\(\Rightarrow2A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot\cdot\cdot\left(3^{64}+1\right)\)

\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\cdot\cdot\cdot\left(3^{64}+1\right)\)

\(=\left(3^4-1\right)\left(3^4+1\right)\cdot\cdot\cdot\left(3^{64}+1\right)\)

\(=\left(3^{64}-1\right)\left(3^{64}+1\right)=\left(3^{128}-1\right)\)

\(\Rightarrow A=\frac{3^{128}-1}{2}\)

làm nhiều rồi 

hehe

hihi

30 tháng 8 2019

3/

a/ \(A=\left(x-y\right)^2+\left(x+y\right)^2.\)

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

\(A=x^2-2xy+y^2+x^2+2xy+y^2\)

\(A=2x^2+2y^2\)

b/ \(B=\left(2a+b\right)^2-\left(2a-b\right)^2\)

\(B=\left(4a^2+4ab+b^2\right)-\left(4a^2-4ab+b^2\right)\)

\(B=4a^2+4ab+b^2-4a^2+4ab-b^2\)

\(B=8ab\)

c/ \(C=\left(x+y\right)^2-\left(x-y\right)^2\)

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

\(C=x^2+2xy+y^2-x^2+2xy-y^2\)

\(C=4xy\)

d/ \(D=\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)

\(D=\left(4x^2-4x+1\right)-2\left(4x^2-12x+9\right)+4\)

\(D=4x^2-4x+1-8x^2+24x-18+4\)

\(D=-4x^2+20x-13\)

27 tháng 1 2020

Khó vl , dẹp mẹ điiii

27 tháng 1 2020

a)     \(A=\left(\frac{1}{4}x-y\right)\left(x^2+4xy+16y^2\right)+4\left(4y^3-\frac{1}{16}x^3+1\right)\)

\(\Leftrightarrow A=\frac{1}{4}\left(x-4y\right)\left(x^2+4xy+16y^2\right)+16y^3-\frac{1}{4}x^3+4\)

\(\Leftrightarrow A=\frac{1}{4}\left(x^3-64y^3\right)+16y^3-\frac{1}{4}x^3+4\)

\(\Leftrightarrow A=\frac{1}{4}x^3-16y^3+16y^3-\frac{1}{4}x^3+4\)

\(\Leftrightarrow A=4\)

b) \(B=2x\left(x-4\right)^2-\left(x+5\right)\left(x-2\right)\left(x+2\right)+2\left(x-5\right)^2-\left(x-1\right)^2\)

\(\Leftrightarrow B=2x\left(x^2-8x+16\right)-\left(x+5\right)\left(x^2-4\right)+2\left(x^2-10x+25\right)-\left(x^2-2x+1\right)\)

\(\Leftrightarrow B=2x^3-16x^2+32x-x^3-5x^2+4x+20+2x^2-20x+50-x^2+2x-1\)

\(\Leftrightarrow B=x^3-20x^2+18x+69\)

c) \(C=\frac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)

\(\Leftrightarrow C=\frac{5x\left(16x^2-25\right)}{\left(x-3\right)\left(3-8+4x\right)}\)

\(\Leftrightarrow C=\frac{5x\left(4x-5\right)\left(4x+5\right)}{\left(x-3\right)\left(4x-5\right)}\)

\(\Leftrightarrow C=\frac{5x\left(4x+5\right)}{x-3}\)

\(\Leftrightarrow C=\frac{20x^2+25x}{x-3}\)

d) \(D=\frac{\left(a-b\right)\left(c-d\right)}{\left(b^2-a^2\right)\left(d^2-c^2\right)}\)

\(\Leftrightarrow D=\frac{\left(a-b\right)\left(c-d\right)}{\left(a^2-b^2\right)\left(c^2-d^2\right)}\)

\(\Leftrightarrow D=\frac{\left(a-b\right)\left(c-d\right)}{\left(a-b\right)\left(a+b\right)\left(c-d\right)\left(c+d\right)}\)

\(\Leftrightarrow D=\frac{1}{\left(a+b\right)\left(c+d\right)}\)

Chúc bạn học tốt !

24 tháng 6 2016

Giúp vs nhé mk sẽ dùng các nick phụ tới tấp cho mí bạn

21 tháng 10 2016

A = 1002 - 992 + 982 - 972 + . . . + 22 - 12

= (100 - 99)(100 + 99) + (98 - 97)(98 + 97) + . . . (2 - 1)(2 + 1)

= 199 + 195 + . . . + 3

= 5050

B = 3(22 + 1)(24 + 1) . . . (264 + 1) + 1

= (22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1)(264 + 1)(264 + 1) + 1

= (24 - 1)(24 + 1)(28 + 1)(216 + 1)(232 + 1)(264 + 1) + 1

= (28 - 1)(28 + 1)(216 + 1)(232 + 1)(264 + 1) + 1

= (216 - 1)(216 + 1)(232 + 1)(264 + 1) + 1

= (232 - 1)(232 + 1)(264 + 1) + 1

= (264 - 1)(264 + 1) + 1

= 2128 - 1 + 1

= 2128

22 tháng 10 2016

Câu C mk chép nhầm đề đó

1. tính a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\) b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\) c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\) d) \(\left(\dfrac{1}{2}x-2y\right)^3\) e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\) f) \(27x^3-8y^3\) g) 4(2x - 3y) - 4 - (2x-3y)2 2. rút gọn a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\) b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\) c)...
Đọc tiếp

1. tính

a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)

b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)

c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)

d) \(\left(\dfrac{1}{2}x-2y\right)^3\)

e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\)

f) \(27x^3-8y^3\)

g) 4(2x - 3y) - 4 - (2x-3y)2

2. rút gọn

a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)

b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)

c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)

d) \(\left(a+2\right)^3-a\left(a-3\right)^2\)

3. c/m các biểu thức sau ko phụ thuộc vào biến x,y

a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)

b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)

c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)

d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)

4. Tìm x

a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)

b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)

c) \(49x^2+14x+1=0\)

d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)

5. c/m biểu thức luôn dương:

a) \(A=16x^2+8x+3\)

b) \(B=y^2-5y+8\)

c) C= \(2x^2-2x+2\)

d) \(D=9x^2-6x+25y^2+10y+4\)

6. Tìm GTLN và GTNN của các biểu thức sau

a) \(M=x^2+6x-1\)

b) \(N=10y-5y^2-3\)

7. thu gọn

a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)

b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)

2
9 tháng 9 2017

Bạn đăng từ từ thôi!

Dài quá

13 tháng 10 2018

\(A=100^2-99^2+98^2-97^2+...+2^2-1^2\)

\(A=\left(100^2-99^2\right)+\left(98^2-97^2\right)+...+\left(2^2-1^2\right)\)

\(A=1.199+1.195+...+3.1\)

\(A=3+7+...+195+199\)

Tổng A có: \(\frac{199-3}{4}+1=50\)( số hạng)

\(\Rightarrow A=\frac{\left(199+3\right).50}{2}=5050\)

Mấy ý kia chốc về lm nốt 

13 tháng 10 2018

\(B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(B=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)

\(B=\left(2^8-1\right)...\left(2^{64}+1\right)+1\)

\(B=2^{64}-1+1\)

\(B=2^{64}\)

14 tháng 7 2016

a) (2+1)(2^2+1)(2^4+1)...(2^32+1)-2^64

=(2+1)(2-1)(2^2+1)(2^4+1)...(2^32+1)-2^64

=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)-2^64

=(2^4-1)(2^4+1)....(2^32+1)-2^64

=......

=(2^32-1)(2^32+1)-2^64

=2^64-1-2^64=-1

b)Đặt A=(5+3)(5^2+3^2)(5^4+3^4)...(5^64+3^64)+(5^128-3^128)/2

đặt B=(5+3)(5^2+3^2)(5^4+3^4)...(5^64+3^64)

\(2B=\left(5-3\right)\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)\)

\(2B=\left(5^2-3^2\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)\)

\(2B=\left(5^4-3^4\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)\)

\(2B=.......\)

2B=(5^64-3^64)(5^64+3^64)

2B=5^128-3^128

B=(5^128-3^128)/2 (thế vào đề bài)

=> A=B+(5^128-3^128)/2=(5^128-3^128)/2+(5^128-3^128)/2=\(\frac{2\left(5^{128}-3^{128}\right)}{2}=\left(5^{128}-3^{128}\right)\)

14 tháng 7 2016

a) A = ( 2-1)(2+1)(22+1)...(232+1)-264

         =(22-1)(22+1)(24+1)... -264

       =....

       =264-1-264=1

câu b tương tự nhá

5 tháng 11 2017

a, \(A=\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}=2^{64}-1-2^{64}=-1\)

b,\(B=\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)

\(=\dfrac{\left(5-3\right)\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)}{2}+\dfrac{5^{128}-3^{128}}{2}\)\(=\dfrac{\left(5^2-3^2\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{64}+3^{64}\right)+5^{128}-3^{128}}{2}\)

\(=\dfrac{\left(5^{64}-3^{64}\right)\left(5^{64}+3^{64}\right)+5^{128}-3^{128}}{2}=\dfrac{2.5^{128}}{2}=5^{128}\)

17 tháng 8 2020

a) \(5x^2-2x\left(3x+\frac{3}{2}\right)=-x^2-3x=-x\left(x+3\right)=-3\left(3+3\right)=-18\)

b) \(3x\left(x-4y\right)-\frac{12}{5}y\left(y-5x\right)=3x^2-\frac{12}{5}y^2=3\left(x^2-\frac{4}{5}y^2\right)\)

\(=3\left(4^2-\frac{4}{5}.5^2\right)=3.\left(-4\right)=-12\)

c) \(\left(x-2\right)^2-\left(x+7\right)\left(x-7\right)=x^2-4x+4-x^2+49=-4x+53=-4.3+53=41\)

d) \(x^2+12x+36=\left(x+6\right)^2=\left(64+6\right)^2=70^2=4900\)

e) \(\left(x-3\right)^2-\left(x-4\right)\left(x+4\right)=x^2-6x+9-x^2+16=-6x+25=-6\left(-1\right)+25\)

= 31

f) \(\left(3x+2y\right)^2-4y\left(3x+y\right)=9x^2+12xy+4y^2-12xy-4y^2=9x^2=9\left(-\frac{1}{3}\right)^2=1\)

17 tháng 8 2020

a, \(5x^2-2x\left(3x+\frac{3}{2}\right)=-x^2-3x\)

Thay x = 3 vào biểu thức trên ta cs : \(-3^2-3.3=-9-9=-18\)

b, \(3x\left(x-4y\right)-\frac{12}{5}y\left(y-5x\right)=3x^2-\frac{12}{5}y^2\)

Thay x = 4 ; y = 5 vào biểu thức trên ta có : \(3.4^2-\frac{12}{5}.5^2=-12\)