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3: =4x^2+4x+1-2
=(2x+1)^2-2
\(=\left(2x+1-\sqrt{2}\right)\left(2x+1+\sqrt{2}\right)\)
4: =x^2+xy-5xy-5y^2
=x(x+y)-5y(x+y)
=(x+y)(x-5y)
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\(a,x^2y-8x+xy-8=xy\left(x+1\right)-8\left(x+1\right)=\left(xy-8\right)\left(x+1\right)\\ b,=\left(x+3y\right)^2-9=\left(x+3y-3\right)\left(x+3y+3\right)\)
\(A=3x^2\left(2x^2-7x-2\right)-6x^2\left(x^2-4x-1\right)-3x^3+15\\ A=6x^4-21x^3-6x^2-6x^4+24x^3+6x^2-3x^3+15\\ A=15\left(đpcm\right)\)
\(Sửa:\left(6x^3-7x^2+2x\right):\left(2x+1\right)\\ =\left(6x^3+3x^2-10x^2-5x\right):\left(2x+1\right)\\ =\left[3x^2\left(2x+1\right)-5x\left(2x+1\right)\right]:\left(2x+1\right)\\ =3x^2-5x\)
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\(=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\\ =\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\\ =\left(x^2+7x+11\right)^2-1-24\\ =\left(x^2+7x+11\right)^2-25\\ =\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\\ =\left(x^2+7x+6\right)\left(x^2+7x+16\right)\\ =\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
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b)\(x^2-x-12\)
\(=x^2+3x-4x-12\)
\(=x\left(x+3\right)-4\left(x+3\right)\)
\(=\left(x-4\right)\left(x+3\right)\)
c sai đề
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a,da thuc nay ko phan tich duoc
b,x2 +9x -10 c,5x2 -3x +2
= x2 - x +10 -10 = 5x2 -5x +2x +2
= x (x-1) +10(x -1) = 5x (x-1 )+2(x+1)
= (x-1)(x+10) = 5x (x-1) -2(x-1)
= (x-1)(5x-2)
d,x2 -13x +42= x2 -7x-6x +42
= x(x-7) -6(x-7)
=(x-7)(x-6)