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nguyễn rhij
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Nguyễn Thị Hồng Nhung
4 tháng 9 2017 lúc 19:25

\(a,\left(a-b+c\right)^2-\left(b-c\right)^2+2ab-2ac\) =\(a^2+b^2+c^2-2ab-2bc+2ac-b^2+2bc-c^2+2ab-2ac\) =\(a^2\) b)\(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\) =\(\left(3x+1\right)^2-2\left(3x+3-2\right)\left(3x+3+2\right)+\left(3x+5\right)^2\) =\(\left(3x+1\right)^2-2\left(\left(3x+3\right)^2-4\right)+\left(3x+5\right)^2\) =\(9x^2+6x+1-18x^2-36x-9+8+9x^2+30x+25\) =25 c)\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)\) =\(\left(2-1\right)\left(2+1\right)\left(2^2+1\right)....\left(2^{64}+1\right)\) =\(\left(2^2-1\right)\left(2^2+1\right)...\left(2^{64}+1\right)\) =... =\(\left(2^{64}-1\right)\left(2^{64}+1\right)=2^{128}-1\) \)

d)Tương tự

erza sarlet
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Nguyễn Thị Hồng Nhung
4 tháng 9 2017 lúc 19:23

\(a,\left(a-b+c\right)^2-\left(b-c\right)^2+2ab-2ac\)

=\(a^2+b^2+c^2-2ab-2bc+2ac-b^2+2bc-c^2+2ab-2ac\)

=\(a^2\)

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

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

=\(\left(3x+1\right)^2-2\left(\left(3x+3\right)^2-4\right)+\left(3x+5\right)^2\)

=\(9x^2+6x+1-18x^2-36x-9+8+9x^2+30x+25\)

=25

c)\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)\)

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

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

=...

=\(\left(2^{64}-1\right)\left(2^{64}+1\right)=2^{128}-1\)

d)Tương tự

Uchiha Sasuke
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mèo miu
27 tháng 7 2021 lúc 16:40

Uzumaki Naruto
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Mai Nguyen Thanh
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Bon Bòn
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Linh
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Trịnh Thùy DƯơng
25 tháng 8 2018 lúc 21:51

rút gọn biểu thức

a)2x(2x−1)2−3x(x+3)(x−3)−4x(x+1)2

=2x(4x2-4x+1)-3x.(x2-9)-4x(x2+2x+1)

=8x3-8x2+2x-3x3-27x-4x3-8x2-4x

=8x3-16x2-7x3-29x

Kiều Vũ Minh Đức
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Yukru
4 tháng 8 2018 lúc 10:11

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

\(=\left[\left(3x+1\right)-\left(3x+5\right)\right]^2\)

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

\(=\left(-4\right)^2\)

\(=16\)

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

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

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

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

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

\(=\dfrac{1}{2}\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)

\(=\dfrac{1}{2}\left(3^{32}-1\right)\left(3^{32}+1\right)\)

\(=\dfrac{1}{2}\left(3^{64}-1\right)\)

Dục Nguyễn
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Nguyễn Lê Phước Thịnh
20 tháng 9 2021 lúc 23:32

Bài 2: 

a: Ta có: \(x\left(2x-1\right)-2x+1=0\)

\(\Leftrightarrow\left(2x-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)