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\(9x^2-12xy+16y^2\)
\(=\left(3x\right)^2-2.\left(3x\right)\left(4y\right)+\left(4y\right)^2\)
\(=\left(3x-4y\right)^2\)
\(P=\frac{x^2}{4}+x^2+1=\left(\frac{x}{2}\right)^2+2.x^2.\frac{1}{2}+1=\left(\frac{x}{2}+1\right)^2\)
2, a, \(9x^2-12x+9=\left(3x\right)^2-2.3.x.3+3^2=\left(3x-3\right)^2\ge0\)
a)\(x^2y-x^3-9y+9y\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(x^2-9\right)\left(y-x\right)\)
\(=\left(x+3\right)\left(x-3\right)\left(y-x\right)\)
\(b,9x^2-1=\left(3x+1\right)\left(3x-1\right)\)
\(c,\left(x-y\right)4-4=\left(x-y-1\right)4\)
\(1,x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right).\)
\(\left(y-x\right)\left(x^2-9\right)=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
\(2,9x^2-1=\left(3x\right)^2-1^2=\left(3x+1\right)\left(3x-1\right)\)
\(3,\left(x-y\right)4-4=4\left(x-y-1\right)\)
\(4,\)\(9\left(x-y\right)^2=3^2\left(x-y\right)^2=\left(3x-3y\right)^2\)
\(5,3x^2-6ab+3b^2-12c^2???\)
\(6,x^2-25+y^2+2xy=\left(x+y\right)^2-25\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
1) \(x^6-x^4-9x^3+9x^2\)
\(=x^2\left(x^4-x^2-9x+9\right)\)
\(=x^2\left[x^2\left(x^2-1\right)-9\left(x-1\right)\right]\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
2) \(x^4-4x^3+8x^2-16x+16\)
\(=x^2\left(x^2+4\right)-4x\left(x^2+4\right)+4\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
3) \(x^4-25x^2+20x-4=x^4+5x^3-2x^2-5x^3-25x^2+10x+2x^2+10x-4\)
\(=x^2\left(x^2+5x-2\right)-5x\left(x^2+5x-2\right)+2\left(x^2+5x-2\right)\)
\(=\left(x^2+5x-2\right)\left(x^2-5x+2\right)\)
4) \(5x\left(x-2y\right)+2\left(2y-x\right)^2\)\(=5x\left(x-2y\right)+2\left(x-2y\right)^2=\left(x-2y\right)\left(5x+2x-4y\right)=\left(x-2y\right)\left(7x-4y\right)\)
5) \(x^2\left(x^2-6\right)-x^2+9=x^4-7x^2+9\)
\(=x^4+x^3-3x^2-x^3-x^2+3x-3x^2-3x+9\)
\(=x^2\left(x^2+x-3\right)-x\left(x^2+x-3\right)-3\left(x^2+x-3\right)\)
\(=\left(x^2+x-3\right)\left(x^2-x-3\right)\)
6) \(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(y-4\right)^2+\left(y-4\right)^3=\left(y-4\right)^2\left(7x+y-4\right)\)
7) \(x^3+2x^2-6x-27=x^3-3x^2+5x^2-15x+9x-27\)
\(=x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)=\left(x-3\right)\left(x^2+5x+9\right)\)
\(a)\) \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)\left(x+1\right)\)
\(=\)\(\left(x+1-x+1\right).\left[\left(x+1\right)^2+\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]-6\left(x^2-1\right)\)
\(=\)\(2\left(x^2+2x+1+x^2-1+x^2-2x+1\right)-6x^2+6\)
\(=\)\(2\left(3x^2+1\right)-6x^2+6\)
\(=\)\(6x^2+2-6x^2+6\)
\(=\)\(8\)
Chúc bạn học tốt ~
sai rồi: (x4 + x2) - (9x3 + 9x)
= x2(x2 + 1) - 9x(x2 + 1)
= (x2 - 9x)(x2 + 1)
uk uk nhưng sao lại ra cái hàng thứ hai ý. giải thích hộ đi