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7x2+x+16
K
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ND
4
TM
1
5 tháng 8 2021
x 16 + x 8 − 2 = ( x 8 ) 2 + x 8 − 2 = ( x 8 − 1 ) ( x 8 + 2 ) = ( x 4 − 1 ) ( x 4 + 1 ) ( x 8 + 2 ) = ( x 2 − 1 ) ( x 2 + 1 ) ( x 4 + 1 ) ( x 8 + 2 ) = ( x − 1 ) ( x + 1 ) ( x 2 + 1 ) ( x 4 + 1 ) ( x 8 + 2 )
GB
1
NH
1
KD
2
NL
Nguyễn Lê Phước Thịnh
CTVHS
29 tháng 9 2025
Đặt \(A=\left(x+3\right)^4+\left(x+1\right)^4-16\)
\(=\left\lbrack\left(x+2\right)+1\right\rbrack^4+\left\lbrack\left(x+2\right)-1\right\rbrack^4-16\)
Đặt b=x+2
=>\(A=\left(b+1\right)^4+\left(b-1\right)^4-16\)
\(=\left(b^2+2b+1\right)^2+\left(b^2-2b+1\right)^2-16\)
\(=\left(b^2+1\right)^2+4b\left(b^2+1\right)+4b^2+\left(b^2+1\right)^2-4b\left(b^2+1\right)+4b^2-16\)
\(=2\left(b^2+1\right)^2+8b^2-16\)
\(=2\left\lbrack\left(b^2+1\right)^2+4b^2-8\right\rbrack\)
\(=2\left\lbrack b^4+2b^2+1+4b^2-8\right\rbrack=2\left(b^4+6b^2-7\right)\)
\(=2\left(b^2+7\right)\left(b^2-1\right)=2\left(b^2+7\right)\left(b-1\right)\left(b+1\right)\)
\(=2\left\lbrack\left(x+2\right)^2+7\right\rbrack\left(x+2-1\right)\left(x+2+1\right)=2\left(x+1\right)\left(x+3\right)\left\lbrack\left(x+2\right)^2+7\right\rbrack\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
29 tháng 9 2025
Đặt \(A=\left(x+3\right)^4+\left(x+1\right)^4-16\)
\(=\left\lbrack\left(x+2\right)+1\right\rbrack^4+\left\lbrack\left(x+2\right)-1\right\rbrack^4-16\)
Đặt b=x+2
=>\(A=\left(b+1\right)^4+\left(b-1\right)^4-16\)
\(=\left(b^2+2b+1\right)^2+\left(b^2-2b+1\right)^2-16\)
\(=\left(b^2+1\right)^2+4b\left(b^2+1\right)+4b^2+\left(b^2+1\right)^2-4b\left(b^2+1\right)+4b^2-16\)
\(=2\left(b^2+1\right)^2+8b^2-16\)
\(=2\left\lbrack\left(b^2+1\right)^2+4b^2-8\right\rbrack\)
\(=2\left\lbrack b^4+2b^2+1+4b^2-8\right\rbrack=2\left(b^4+6b^2-7\right)\)
\(=2\left(b^2+7\right)\left(b^2-1\right)=2\left(b^2+7\right)\left(b-1\right)\left(b+1\right)\)
\(=2\left\lbrack\left(x+2\right)^2+7\right\rbrack\left(x+2-1\right)\left(x+2+1\right)=2\left(x+1\right)\left(x+3\right)\left\lbrack\left(x+2\right)^2+7\right\rbrack\)
K
1
BT
4
7 tháng 1 2022
\(\left(x+2\right)^2-16\\ \backslash=\left(x+2-4\right)\left(x+2+4\right)\\ =\left(x-2\right)\left(x+6\right)\)
PT
1
MT
1
P
10 tháng 6 2023
\(x^4+3x^3+12x-16\)
\(=x^4+4x^3+4x^2+16x-x^3-4x^2-4x-16\)
\(=x\left(x^3+4x^2+4x+16\right)-\left(x^3+4x^2+4x+16\right)\)
\(=\left(x-1\right)\left(x^3+4x^2+4x+16\right)\)
\(=\left(x-1\right)\left[x^2\left(x+4\right)+4\left(x+4\right)\right]\)
\(=\left(x-1\right)\left(x+4\right)\left(x^2+4\right)\)