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Bài 1 :
Ta có : \(VP=\left(a+b\right)^4=\left(a+b\right)\left(a+b\right)^3\)
\(=\left(a+b\right)\left(a^3+3a^2b+3ab^2+b^3\right)=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)
=> HĐT ko đc CM
Bài 2 :
a, \(\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)+7\)
\(=x^3+2x^2+4x-2x^2-4x-8-x+1+7=x^3-x=x\left(x^2-1\right)\)
Sửa đề : b, \(8\left(x-1\right)\left(x^2+x+1\right)-\left(2x-1\right)\left(4x^2+2x+1\right)\)
\(=8\left(x^3-1\right)-8x^3+1=8x^3-8-8x^3+1=-7\)
Xin phép chủ nahf cho mjnh sửa đề:D
\(\left(a+b\right)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)
a,\(\left(a+b\right)^4\)
\(=\left[\left(a+b\right)^2\right]^2\)
\(=\left(a^2+2ab+b^2\right)^2\)
\(=\left[\left(a^2+2ab\right)+b^2\right]^2\)
\(=\left(a^2+2ab\right)^2+2\left(a^2+2ab\right)b^2+b^4\)
\(=a^4+4a^3b+4a^2b^2+2a^2b^2+4ab^3+b^4\)
\(=a^4+4a^3b+6a^2b^2+4ab^3+b^4\)
Bài 2:
a,\(\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)+7\)
\(=\left(x^3-8\right)-\left(x-1\right)+7\)
b,\(8\left(x-1\right)\left(x^2+x+1\right)-\left(2x-1\right)\left(4x^2+2x-1\right)\)
\(=8\left(x^3-1\right)-\left(8x^3-1\right)\)
\(=8x^3-8-8x^3+1\)
\(=-7\)
a, \(\left(x+3\right)^3-\left(x+2\right)\left(x-2\right)-6x^2-20\)
\(=x^3+9x^2+27x+27-\left(x^2-4\right)-6x^2-20\)
\(=x^3+9x^2+27x+27-x^2+4+6x^2+20\)
\(=x^3+14x^2+27x+51\)
b, \(\left(2x+3\right)\left(4x^2-6x+9\right)-\left(2x-3\right)\left(4x^2+6x+9\right)\)
\(=8x^3-12x^2+18x+12x^2-18x+18-\left(8x^3+12x^2+18x-12x^2-18x-18\right)\)
\(=8x^3+18-8x^3+18=36\)
c, \(\left(2x-1\right)\left(4x^2+2x+1\right)\left(2x+1\right)\left(4x^2-2x+1\right)\)
\(=\left(8x^3+4x^2+2x-4x^2-2x-1\right)\left(8x^3-4x^2+2x+4x^2-2x+1\right)\)
\(=\left(8x^3-1\right)\left(8x^3+1\right)=\left(8x^3\right)^2-1\)
\(=64x^5-1\)
d, \(\left(x+4\right)\left(x^2-4x+16\right)-\left(50+x^2\right)\)
\(=x^3-4x^2+16x+4x^2-16x+64-50-x^2\)
\(=x^3-x^2+14\)
Chúc bạn học tốt!!!
\(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2=4x^2+1+8x^2-2+4x^2-1=16x^2-2\)\(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)=x^3+2x^2-x-2-\left(x^3+2x^2+4x-2x^2-4x-8\right)=x^3+2x^2-x-2-x^3-2x^2-4x+2x^2+4x+8=2x^2-x+6\)