PTĐTTNT : n^2 + 10
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\(=81x^2-\left(z+3y\right)^2\)
\(=\left(9x+z+3y\right)\left(9x-z-3y\right)\)
\(=x^2-xm-xn+mn=x\left(x-m\right)-n\left(x-m\right)=\left(x-n\right)\left(x-m\right)\)
a) \(x^3-3x^2+1-3x=\left(x^3+1\right)-\left(3x^2+3x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
b) \(3x^2-7x-10=3x^2+3x-10x-10\)
\(=3x\left(x+1\right)-10\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-10\right)\)
a) \(x^3-3x^2-3x+1=\left(x^3+1\right)-\left(3x^2+3x\right)\)
= \(\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
= \(\left(x+1\right)\left(x^2-x+1-3x\right)\)
= \(\left(x+1\right)\left(x^2-4x+1\right)\)
b) \(3x^2-7x-10=\left(3x^2+3x\right)-\left(10x+10\right)\)
= \(3x\left(x+1\right)-10\left(x+1\right)\)
= \(\left(x+1\right)\left(3x-10\right)\)
x^10 + x^5 + 1
= x^10 + x^9 - x^9 + x^8 - x^8 + x^7 - x^7 + x^6 - x^6 + x^5 + x^5 - x^5 + x^4 - x^4 + x^3 - x^3 + x^2 - x^2 + x - x + 1
= (x^10 + x^9 + x^8) - (x^9 + x^8 + x^7) + (x^7 + x^6 + x^5) - (x^6 + x^5 + x^4) + (x^5 + x^4 + x^3) - (x^3 + x^2 + x) + (x^2 + x + 1)
= x^8 (x^2 + x + 1) - x^7 (x^2 + x + 1) + x^5 (x^2 + x + 1) - x^4 (x^2 + x + 1) + x^3 (x^2 + x + 1) - x (x^2 + x + 1) + (x^2 + x + 1)
= (x^2 + x + 1) (x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)
a) \(x^2+7x+12\)
\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
b) \(3x^2-5x+2\)
\(=3x^2-3x-2x+2\)
\(=3x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-2\right)\)
\(=3\left(x-y\right)+2\left(x-y\right)\left(x+y\right)=\left(x-y\right)\left(3+2x+2y\right)\)