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23 tháng 9 2017

\(\text{a) }\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(6x+1\right)\left(6x-1\right)\\ =\left[\left(6x+1\right)-\left(6x-1\right)\right]^2\\ =\left[6x+1-6x+1\right]^2\\ =2^2\\ =4\)

\(\text{b) }3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\\ =\left(2^{16}-1\right)\left(2^{16}+1\right)\\ =2^{32}-1\)

AH
Akai Haruma
Giáo viên
4 tháng 8 2021

Bài 1 không có cơ sở để tính biểu thức.

AH
Akai Haruma
Giáo viên
4 tháng 8 2021

Bài 2:

a. 

$(6x+1)^2+(6x-1)^2-2(6x+1)(6x-1)$

$=[(6x+1)-(6x-1)]^2=2^2=4$

b.

$3(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)$

$=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)$

$=(2^4-1)(2^4+1)(2^8+1)(2^{16}+1)$

$=(2^8-1)(2^8+1)(2^{16}+1)$
$=(2^{16}-1)(2^{16}+1)=2^{32}-1$

c.

$2C=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^{16}+1)$

$=(5^4-1)(5^4+1)(5^8+1)(5^{16}+1)$

$=(5^8-1)(5^8+1)(5^{16}+1)$
$=(5^{16}-1)(5^{16}+1)=5^{32}-1$

$\Rightarrow C=\frac{5^{32}-1}{2}$

2 tháng 11 2015

\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

\(=\left(6x+1-6x+1\right)^2\)

\(=2^2=4\)

\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1\)

 

22 tháng 8 2015

a) \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

 \(=\left(6x+1\right)\left(6x+1\right)+\left(6x-1\right)\left(6x-1\right)-2\left(1+6x\right)\left(6x-1\right)\)

\(=\left(6x+1\right)\left(6x+1\right)+\left(6x-1\right)\left[\left(6x-1\right)-2\left(1+6x\right)\right]\)

\(=\left(6x+1\right)\left(6x+1\right)+\left(6x-1\right)\left(6x-1-2-12x\right)\)

\(=36x^2+12x+1+\left(6x-1\right)\left(-6x-3\right)\)

\(=36x^2+12x+1+\left(-36x^2-12x+3\right)\)

\(=36x^2+12x+1-36x^2-12x+3\)

\(=4\)

9 tháng 8 2017

câu b làm thế nào vậy

a) Ta có: \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

\(=\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)

\(=\left(6x+1-6x+1\right)^2=2^2=4\)

b) Ta có: \(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)

\(=2x^3-3x-5x^3-x^2+x^2\)

\(=-3x-3x^3\)

c) Ta có: \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=24-11x\)

d) Ta có: \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1\)

19 tháng 12 2019

a) \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

\(=36x^2+12x+1+36x^2-12x+1-72x^2+2\)

\(=4\)

c) \(x\left(2x^2-3\right)-x^2\left(5x+1\right)+x^2\)

\(=2x^3-3x-5x^3-x^2+x^2\)

\(=-3x^3-3x\)

d) \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=-11x+24\)

30 tháng 3 2020

a) (6x+1)2 + (6x-1)2 - 2(1+6x)(6x-1)

= (6x+1+6x-1)2 

=144x2

b) x(2x2 -3) - x2(5x+1) +x2

=2x3 - 3x - 5x3 -x2+x2

=-3x3-3x

=-3x(x2+1)

c) 3(22+1)(24+1)(28+1)(216+1)

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

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

= (28-1)(28+1)(216+1)

= (216-1)(216+1)

= 232 -1

d) 3x(x-2) - 5x(1-x) - 8(x2 -3)

= 3x2-6x - 5x + 5x2 - 8x2 +24 

= -11x +24

30 tháng 3 2020

a) = (6x+1)-2(6x+1)(6x-1)+(6x-1)2=(6x+1-6x+1)2=22=4

7 tháng 7 2017

\(a,\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

\(=36x^2+12x+1+36x^2-12x+1-2\cdot\left(36x^2-1\right)\)

\(=72x^2+2-72x^2+2=4\)

7 tháng 7 2017

Ta có : 3(22 + 1)(24 + 1)(x8 + 1)(216 + 1)

= (24 - 1)(24 + 1)(28 + 1)(216 + 1)

= (28 - 1)(28 + 1)(216 + 1)

= (216 - 1)(216 + 1)

= 232 - 1

4 tháng 9 2017

a, Áp dụng hằng đẳng thức số 2 ta có

[6x+1-(6x+1)]2=(6x+1-6x-1)2=0

b, (22-1)(22+1)(24+1)(28+1)(216+1)

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

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

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