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\(\dfrac{xy}{2}-x+\dfrac{x^2}{4}=x\left(\dfrac{y}{2}-1+\dfrac{x}{4}\right)\)
a) \(x\left(x+4\right)\left(x-4\right)-\left(x^2-1\right)\left(x^2+1\right)\)
\(=x\left(x^2-16\right)-\left(x^4-1\right)\)
\(=x^3-16x-x^4+1\)
bạn ktra lại đề
b) \(x^4+2x^3+5x^2+4x-12\)
\(=x^3\left(x-1\right)+3x^2\left(x-1\right)+8x\left(x-1\right)+12\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3+3x^2+8x+12\right)\)
\(=\left(x-1\right)\left[x^2\left(x+2\right)+x\left(x+2\right)+6\left(x+2\right)\right]\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
\(\left(x+1\right)^4+\left(x^2+x+1\right)^2\)
\(=2x^4+6x^3+9x^2+6x+2\)(bạn nhân phá ngoặc rồi thu gọn nhé)
\(=\left(2x^4+2x^3+x^2\right)+\left(4x^3+4x^2+2x\right)+\left(4x^2+4x+2\right)\)
\(=x^2\left(2x^2+2x+1\right)+2x\left(2x^2+2x+1\right)+2\left(2x^2+2x+1\right)\)
\(=\left(x^2+2x+2\right)\left(2x^2+2x+1\right)\)
a) \(x^3+9x^2+27x+27=\left(x+3\right)^3\)
b) \(3\sqrt{3x^3}+18x^2+12\sqrt{3x}+8=\left(\sqrt{3x}+2\right)^3\)
c) \(\dfrac{1}{4}-x^2=\left(\dfrac{1}{2}-x\right)\left(\dfrac{1}{2}+x\right)\)
ta có: \(x^2\left(x+4\right)^2-\left(x+4\right)^2-\left(x^2-1\right)\)
\(=\left(x+4\right)^2.\left(x^2-1\right)-\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(\left(x+4\right)^2-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+4-1\right)\left(x+4+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+5\right)\)
Cho mình nhé hihi!!!
x2(x+4)2-(x+4)2-(x2-1)
=(x+4)2 (x2-1)-(x2-1)
=(x2-1)(x2+8x+16-1)
=(x-1)(x+1)(x2+8x+15)
Mình mới lớp 7 nên chỉ giải được 1 bài thôi!
\(3x^2-7x+2=3x^2-\left(6x+1x\right)+2=3x^2-6x-1x+2\)
\(3x\left(x-2\right)-1\left(x-2\right)=\left(x-2\right)\left(3x-1\right)=3\left(x-2\right)\left(x-\frac{1}{3}\right)\)
