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\(a^8+a^4+1=\left(a^8+2a^4+1\right)-a^4\)
\(=\left(a^4+1\right)^2-a^4\)
\(=\left(a^4-a^2+1\right)\left(a^4+a^2+1\right)\)
\(=\left[\left(a^4-2a^2+1\right)-a^2\right]\left(a^4+a^2+1\right)\)
\(=\left[\left(a^2-1\right)^2-a^2\right]\left(a^4+a^2+1\right)\)
\(=\left(a^2-a-1\right)\left(a^2-a+1\right)\left(a^4+a^2+1\right)\)
*\(a^8+a^7+1=a^8+a^7+a^6-a^6+a^5-a^5+a^4-a^4+a^3-a^3+a^2-a^2+a-a+1\)\(=\left(a^8+a^7+a^6\right)+\left(a^5+a^4+a^3\right)+\left(a^2+a+1\right)-\left(a^6+a^5+a^4\right)-\left(a^3+a^2+a\right)\)\(=a^6\left(a^2+a+1\right)+a^3\left(a^2+a+1\right)+\left(a^2+a+1\right)-a^4\left(a^2+a+1\right)-a\left(a^2+a+1\right)\)\(=\left(a^2+a+1\right)\left(a^6-a^4+a^3-a+1\right)\)
x\(^2\)-(a+b)x+ab
= x\(^2\)-ax-bx+ab
= x(x-a) - b(x-a)
= ( x-a).( x-b)
ax-2x-a\(^2\)+2a
= x(a-2) - a(a-2)
= (a-2).( x-a)
\(B=x^4+3x^3-x^2+3x^3+9x^2-3x-x^2-3x+1\)
\(=\left(x^2+3x-1\right)^2\)
\(=\left(a+b\right)^2+2\left(a+b\right)c+c^2+\left(a+b\right)^2-2\left(a+b\right)c+c^2-4c^2\)
\(=2\left(a+b\right)^2-2c^2=2\left[\left(a+b\right)^2-c^2\right]=2\left(a+b+c\right)\left(a+b-c\right)\)
Mình đã làm bài này rồi.
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\(\left(a+b+c\right)^2+\left(a+b-c\right)^2-4c^2\)
\(=\left[\left(a+b+c\right)^2-\left(2c\right)^2\right]+\left(a+b-c\right)^2\)
\(=\left(a+b+3c\right)\left(a+b-c\right)+\left(a+b-c\right)^2\)
\(=\left(a+b-c\right)\left(a+b+3c+a+b-c\right)\)
\(=\left(a+b-c\right)\left(2a+2b+2c\right)\)
\(=2\left(a+b-c\right)\left(a+b+c\right)\)
\(a^6+a^4+a^2b^2+b^4-b^6\)
\(=(a^2)^3-(b^2)^3+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2)(a^4+a^2b^2+b^4)+(a^4+a^2b^2+b^4)\)
\(=(a^2-b^2+1)(a^4+a^2b^2+b^4)\)
\(=(a^4+2a^2b^2+b^4-a^2b^2)(a^2-b^2+1)\)
\(=(a^2+ab+b^2)(a^2-ab+b^2)(a^2-b^2+1)\)
\(a^6+a^2b^2+a^4+b^2-b^6\)
\(=a^4\left(a^2+b^2\right)+a^2\left(a^2+b^2\right)-b^6\)
\(=\left(a^2+b^2\right)+\left(a^4+a^2\right)-b^6\)