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3(x+3)-x2+9
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DN
2
12 tháng 9 2021
\(=\left(x+3\right)^6-y^6\\ =\left[\left(x+3\right)^3-y^3\right]\left[\left(x+3\right)^3+y^3\right]\\ =\left(x+3-y\right)\left[\left(x+3\right)^2+y\left(x+3\right)+y^2\right]\left(x+3+y\right)\left[\left(x+3\right)^2-y\left(x+3\right)+y^2\right]\\ =\left(x+y+3\right)\left(x-y+3\right)\left(x^2+6x+9+xy+3y+y^2\right)\left(x^2+6x+9-xy-3y+y^2\right)\)
TG
12 tháng 9 2021
\(\left(x^2+6x+9\right)^3-\left(y^2\right)^3=\left(x^2+6x+9-y^2\right)\left[\left(x^2+6x+9\right)^2+\left(x^2+6x+9\right)y^2+y^4\right]\)
\(=\left[\left(x+3\right)^2-y^2\right]\left\{\left[\left(x^2+6x+9\right)^2+2\left(x^2+6x+9\right)y^2+y^4\right]-\left(x^2+6x+9\right)y^2\right\}\)
\(=\left(x+3-y\right)\left(x+3+y\right)\left[\left(x^2+6x+9+y^2\right)^2-\left(x+3\right)^2y^2\right]\)
\(=\left(x+3-y\right)\left(x+3+y\right)\left[\left(x^2+6x+9+y^2\right)-\left(x+3\right)y\right]\left(x^2+6x+9+y^2\right)+\left(x+3\right)y\)
\(=\left(x+3-y\right)\left(x+3+y\right)\left(x^2+6x+9+y^2-xy-3y\right)\left(x^2+6x+9+y^2+xy+3y\right)\)
1 tháng 9 2021
\(x^2\left(x+4\right)^2-\left(x+4\right)^2-\left(x^2-1\right)\\ =\left(x+4\right)^2\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^2-1\right)\left[\left(x+4\right)^2-1\right]\\ =\left(x-1\right)\left(x+1\right)\left(x+4-1\right)\left(x+4+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+5\right)\)
4 tháng 9 2021
Ta có: (x2+6x-5)(x2+6x+3)-20
= [(x2+6x-1)-4][(x2+6x-1)+4]-20
= (x2+6x-1)2-16-20
= (x2+6x-1)2-36
= (x2+6x-7)(x2+6x-5)
= (x+7)(x-1)(x2+6x-5)
4 tháng 9 2021
\(\left(x^2+6x-5\right)\left(x^2+6x+3\right)\\ =\left(x^2+6x-1\right)^2-16-20\\ =\left(x^2+6x-1\right)^2-36\\ =\left(x^2+6x-1-6\right)\left(x^2+6x-1+6\right)\\ =\left(x^2+6x-7\right)\left(x^2+6x+5\right)\\ =\left(x-1\right)\left(x+7\right)\left(x+1\right)\left(x+5\right)\)
4 tháng 9 2021
\(\left(x^2+5x-3\right)\left(x^2+5x-5\right)-15=\left(x^2+5x-3\right)\left(x^2+5x-3-2\right)-15=\left(x^2+5x-3\right)^2-2\left(x^2+5x-3\right)+1-16=\left(x^2+5x-3-1\right)^2-4^2=\left(x^2+5x-4\right)^2-4^2=\left(x^2+5x-8\right)\left(x^2+5x\right)=x\left(x+5\right)\left(x^2+5x-8\right)\)
4 tháng 9 2021
\(\left(x^2+5x-3\right)\left(x^2+5x-5\right)-15\)
\(=\left(x^2+5x\right)^2-8\left(x^2+5x\right)-15\)
\(=x\left(x+5\right)\left(x^2+5x-8\right)\)
DN
1
31 tháng 8 2021
\(x^2+3y^2-4xy+10x-12y+9\)
\(=\left(x^2-xy+x\right)+9x-3xy+3y^2-12y+9\)
\(=\left(x^2-xy+x\right)+\left(9x-9y+9\right)-3xy+3y^2-3y\)
\(=\left(x^2-xy+x\right)+\left(9x-9y+9\right)-\left(3xy-3y^2+3y\right)\)
\(=x\left(x-y+1\right)+9\left(x-y+1\right)-3y\left(x-y+1\right)\\ =\left(x-y+1\right)\left(x+9-3y\right)\)
DN
2
4 tháng 9 2021
\(x^2-x-2020.2021=x^2+2020x-2021x-2020.2021=x\left(x+2020\right)-2021\left(x+2020\right)=\left(x+2020\right)\left(x-2021\right)\)
4 tháng 9 2021
\(x^2-x-2020\cdot2021\)
\(=\left(x-2021\right)\left(x+2020\right)\)
DN
3
4 tháng 9 2021
\(\left(x^2+x\right)^2+4x^2+4x-12=\left[\left(x^2+x\right)^2+4\left(x^2+x\right)+4\right]-16=\left(x^2+x+2\right)-4^2=\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)=\left(x^2+x-2\right)\left(x^2+x+6\right)=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
LN
4 tháng 9 2021
\(\left(x^2+x\right)^2+4x^2+4x-12\\ =\left(x^2+x+2\right)-4\\ =\left(x^2+x-2\right)\left(x^2+x+6\right)\)
4 tháng 9 2021
\(=\left(x^2+5x+8\right)\left(x^2+4x+2x+8\right)=\left(x^2+5x+8\right)\left[x\left(x+4\right)+2\left(x+4\right)\right]\)
\(=\left(x^2+5x+8\right)\left(x+2\right)\left(x+4\right)\)
4 tháng 9 2021
\(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2=\left(x^2+4x+8\right)^2+2x\left(x^2+4x+8\right)+x\left(x^2+4x+8\right)+2x^2\)
\(=\left(x^2+4x+8\right)\left(x^2+4x+8+2x\right)+x\left(x^2+4x+8+2x\right)\)
\(=\left(x^2+4x+8\right)\left(x^2+6x+8\right)+x\left(x^2+6x+8\right)\)
\(=\left(x^2+4x+8+x\right)\left(x^2+6x+8\right)=\left(x^2+5x+8\right)\left(x^2+6x+8\right)\)
DN
3
DN
3
3(x-3)-x²+9
=3(x-3)-(x²-9)
=3(x-3)-(x-3)(x+3)
=(x-3)(3-x-3)
=-x(x-3)
3(x+3)-x2+9
=3(x+3)+(3+x)(3-x)
=(3+x)(3+3-x)
=(3+x)(6-x)