Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1: \(3x\left(x-1\right)+7x^2\left(x-1\right)\)
\(=\left(x-1\right)\left(7x^2+3x\right)\)
=x(7x+3)(x-1)
2: \(9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15\right)^2-\left(x-7\right)^2\)
=(3x+15+x-7)(3x+15-x+7)
=(4x+8)(2x+22)
\(=4\left(x+2\right)\cdot2\cdot\left(x+11\right)=8\left(x+2\right)\left(x+11\right)\)
3: \(x^2-2xy+y^2-xz+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
=(x-y)(x-y-z)
4: \(\left(x^2+2x\right)^2-2x^2-4x-3\)
\(=\left(x^2+2x\right)^2-2\cdot\left(x^2+2x\right)-3\)
\(=\left(x^2+2x-3\right)\left(x^2+2x+1\right)=\left(x+3\right)\left(x-1\right)\left(x+1\right)^2\)
5: \(9x^2y^2+15x^2y-21xy^2\)
\(=3xy\cdot3xy+3xy\cdot5x-3xy\cdot7y\)
=3xy(3xy+5x-7y)
6: \(x^3-2x^2y+xy^2-9xy^4\)
\(=x\left(x^2-2xy+y^2-9y^4\right)\)
\(=x\left\lbrack\left(x-y\right)^2-\left(3y^2\right)^2\right\rbrack=x\left(x-y-3y^2\right)\left(x-y+3y^2\right)\)
7: \(x^2+x-12\)
\(=x^2+4x-3x-12\)
=x(x+4)-3(x+4)
=(x+4)(x-3)
8: (x+1)(x+3)(x+5)(x+7)+15
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
\(=\left(x^2+8x+7\right)^2+8\left(x^2+8x+7\right)+15\)
\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)
6: \(\left(2x^3-5x^2+6x-15\right):\left(2x-5\right)\)
\(=\frac{x^2\left(2x-5\right)+3\left(2x-5\right)}{2x-5}\)
\(=\frac{\left(2x-5\right)\left(x^2+3\right)}{2x-5}=x^2+3\)
2: \(\frac{2x^4-5x^2+x^3-3-3x}{x^2-3}\)
\(=\frac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)
\(=\frac{2x^2\left(x^2-3\right)+x\cdot\left(x^2-3\right)+\left(x^2-3\right)}{x^2-3}=2x^2+x+1\)
5: \(\left(2x^3+5x^2-2x+3\right):\left(2x^2-x+1\right)\)
\(=\frac{2x^3-x^2+x+6x^2-3x+3}{2x^2-x+1}=\frac{\left(2x^2-x+1\right)\left(x+3\right)}{2x^2-x+1}\)
=x+3
3: \(\left(x-y-z\right)^5:\left(x-y-z\right)^3=\left(x-y-z\right)^{5-3}=\left(x-y-z\right)^2\)
1: \(\left(x^3-3x^2+x-3\right):\left(x-3\right)\)
\(=\frac{x^2\left(x-3\right)+\left(x-3\right)}{x-3}=x^2+1\)
