Rút gọn biểu thức
3(2^2 +1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)
Những câu hỏi liên quan
Rút gọn biểu thức: (3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
goi y nha A=1/2.(3^2-1)(3^2+1)....(3^32+1)
Rút gọn biểu thức sau:
3.(22+1)(24+1)(28+1)(216+1)(232+1)
( bài này áp dụng hằng đẳng thức \(a^2-b^2=\left(a+b\right)\left(a-b\right)\)
Ta có
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(=2^{64}-1\)
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3.(22+1)(24+1)(28+1)(216+1)(232+1)
=(22-1)(22+1)(24+1)(28+1)(216+1)(232+1)
=(24-1)(24+1)(28+1)(216+1)(232+1)
=(28-1)(28+1)(216+1)(232+1)
=(216-1)(216+1)(232+1)
=(232-1)(232+1)
=264-1
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Bình luận (4)
Rút gọn biểu thức:
a) (x-2)(x^2-2x+4)(x+2)(x^2+2x+4)
b)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
rút gọn biểu thức : A = 3( 22 + 1)( 24 + 1)( 28 + 1)( 216 + 1)( 232 + 1)
\(A=3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\)
\(=\left(2^{32}-1\right)\left(2^{32}+1\right)\)
\(=2^{64}-1\)
A = 3( 22 + 1 )( 24 + 1 )( 28 + 1 )( 216 + 1 )( 232 + 1 )
= ( 22 - 1 )( 22 + 1 )( 24 + 1 )( 28 + 1 )( 216 + 1 )( 232 + 1 )
= ( 24 - 1 )( 24 + 1 )( 28 + 1 )( 216 + 1 )( 232 + 1 )
= ( 28 - 1 )( 28 + 1 )( 216 + 1 )( 232 + 1 )
= ( 216 - 1 )( 216 + 1 )( 232 + 1 )
= ( 232 - 1 )( 232 + 1 )
= 264 - 1
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RÚT GỌN BIỂU THỨC SAU
3(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
3(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(22-1)(22+1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(24-1)(24+1)(28+1)(216+1)(232+1)(264+1)
=(28-1)(28+1)(216+1)(232+1)(264+1)
=(216-1)(216+1)(232+1)(264+1)
=(232-1)(232+1)(264+1)
=(264-1)(264+1)
=(2128-1)
Nếu thấy đúng thì thích cho mình nha
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Rút gọn biểu thức sau: 8.(32+1).(34+1).(38+1).(316+1)-332
\(8.\left(3^2+1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)
\(=\left(3^2-1\right).\left(3^2+1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)
\(=\left(3^4-1\right).\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)
\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)-3^{32}\)
\(=\left(3^{16}-1\right)\left(3^{16}+1\right)-3^{32}=3^{32}-1-3^{32}=-1\)
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rút gọn biểu thức :
3(2^2+1)(2^4+1)(2^8+1)(2^16+1)
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
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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
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Rút gọn biểu thức
3(2^2 +1)(2^4+1)(2^8+1)(2^16+1)
Rút gọn biểu thức
(3+1).(3^2+1).(3^4+1).(3^8+1).(3^16+1).(3^32+1)
Giúp mình vs nha <3
Đặt \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\).Ta có :
\(=>\left(3-1\right)A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(=>2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(=>2A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
...............................................................................
Cuối cùng \(=>2A=3^{64}-1\).
\(=>A=\frac{3^{64}-1}{2}\)
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Đặt \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\Rightarrow2A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(=...........................................\)
\(=\left(3^{32}-1\right)\left(3^{32}+1\right)=3^{64}-1\)
\(\Rightarrow A=\frac{3^{64}-1}{2}\)
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Bình luận (1)
Rút gọn biểu thức sau:
A=3.(2^2+1).(2^4+1).(2^8+2).(2^16+1)
