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Bài 1:
a) \((x-5)(3x+3)-3x(x-3)+3x+7\)
\(=3(x-5)(x+1)-3x(x-3)+3x+7\)
\(=3(x^2+x-5x-5)-(3x^2-9x)+3x+7\)
\(=3(x^2-4x-5)-(3x^2-9x)+3x+7\)
\(=-8\)
b) \((x-3)(x^2+3x+9)-(54+x^3)\)
\(=(x-3)(x^2-3.x+3^2)-(54+x^3)\)
\(=x^3-3^3-(54+x^3)=-81\)
c) Sửa đề:
\((3x+y)(9x^2-3xy+y^2)-(3x-y)(9x^2+3xy+y^2)\)
\(=(3x+y)[(3x)^2-3x.y+y^2]-(3x-y)[(3x)^2+3x.y+y^2]\)
\(=(3x)^3+y^3-[(3x)^3-y^3]\)
\(=2y^3\)
Câu 2:
\(a)14x^2y^2-21xy^2+28x^2y\)
\(=7xy(2xy-3y+4x)\)
b) \((x+y)^2-4x^2\)\(=(x+y)^2-(2x)^2=(x+y-2x)(x+y+2x)\)
\(=(y-x)(3x+y)\)
c) \(2x^2-2xy-5x+5y\)
\(=(2x^2-2xy)-(5x-5y)\)
\(=2x(x-y)-5(x-y)=(x-y)(2x-5)\)
d) \(2xy-x^2-y^2+16\)
\(=16-(x^2+y^2-2xy)=4^2-(x-y)^2\)
\(=[4-(x-y)][4+(x-y)]=(4-x+y)(4+x-y)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\left(2x+1\right)^2+2.\left(2x+1\right)+1=\left(2x+2\right)^2\)
b) \(\left(3x-2y\right)^2+4.\left(3x-2y\right)+4\)
\(=\left(3x-2y\right)^2+2.\left(3x-2y\right).2+2^2\)
\(=\left(3x-2y+2\right)^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
a: \(A=\left(x+1\right)^3+5=20^3+5=8005\)
b: \(B=\left(x-1\right)^3+1=10^3+1=1001\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\left(x+3\right).\left(x^2-3x+9\right)-\left(54+x^3\right)=x^3+27-54-x^3=-27.\)
\(b,8x^3+y^3-8x^3+y^3=2y^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\left(3x+1\right)^3=9x^3+9x^2+9x+1\)
\(b,\left(\frac{2}{3}x+1\right)^2=\frac{4}{9}x^2+\frac{4}{3}x+1\)
\(c,\left(x-y\right)^2-\left(x+y\right)^2=\left(x-y-x-y\right)\left(x-y+x+y\right)=-2y\cdot2x=-4xy\)
\(d,\left(x+y\right)^2-\left(x-y\right)^2=\left(x+y-x+y\right)\left(x+y+x-y\right)=2y\cdot2x=4xy\)