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Đặt x2+10x+5=a.Ta có biểu thức là : a(a+8)+16=a2+8a+16=(a+4)2=(x2+10x+9)2
\(x^4+5x^3+10x-4\)
\(=x^4+5x^3-2x^2+2x^2+10x-4\)
\(=x^2\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+2\right)\left(x^2+5x-2\right)\)
Mình cũng vừa làm được cách 2:
\(x^4+5x^3+10x-4\)
=\(x^4-4+5x^3+10x\)
=\(\left(x^2+2\right)\left(x^2-2\right)+5x\left(x^2+2\right)\)
=\(\left(x^2+2\right)\left(x^2+5x-2\right)\)
\(B=x^8+2x^5-2x^4+x^2-2x-100+10x\left(x^4+x\right)+\left(5x-1\right)^2\)
\(=x^8+2x^5-2x^4+x^2-2x-100+10x^5+25x^2-10x+1\)
\(=x^8+12x^5-2x^4+36x^2-12x-99\)
\(=x^8+6x^5+9x^4+6x^5+36x^2+54x-11x^4-66x-99\)
\(=x^4\left(x^4+6x+9\right)+6x\left(x^4+6x+9\right)-11\left(x^4+6x+9\right)\)
\(=\left(x^4+6x+9\right)\left(x^4+6x-11\right)\)
= (x^4-4x^3)+(3x^3-12x^2)+(2x^2-8x)-(2x-8)
= x^3.(x-4)+3x^2.(x-4)+2x.(x-4)-2.(x-4)
= (x-4).(x^3+3x^2+2x-2)
Tk mk nha
\(x^2-10x+16\)
\(=x^2-2x-8x+16\)
\(=x\left(x-2\right)-8\left(x-2\right)=\left(x-2\right)\left(x-8\right)\)
\(x^2-8x+15\)
\(=x^2-3x-5x+15\)
\(=x\left(x-3\right)-5\left(x-3\right)=\left(x-3\right)\left(x-5\right)\)
c) x2 -10x + 16
= x2 - 2x - 8x + 16
= x.(x-2) - 8.(x-2)
= (x-2).(x-8)
d) x2 - 8x + 15
= x2 - 3x - 5x + 15
= x.(x-3) - 5.(x-3)
= (x-3).(x-5)
x^2 - 10x + 24
= x^2 - 4x - 6x + 24
= x(x - 4) - 6(x - 4)
= (x - 6)(x - 4)
\(x^2-y^2+10x-6y+16\)
\(=\left(x^2+10x+25\right)-\left(y^2+6y+9\right)\)
\(=\left(x+5\right)^2-\left(y+3\right)^2\)
\(=\left(x+5-y-3\right)\left(x+5+y+3\right)\)
\(=\left(x-y+2\right)\left(x+y+8\right)\)
\(x^2-10x+16\)
\(=\left(x^2-2x\right)-\left(8x-16\right)\)
\(=x.\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x-8\right)\)
Tham khảo nhé~