1) 3x³ y²-6x.x.y³ + 9x²y² 2) 12x²y – 18xy² – 30y² 3) 5(x-y) – y(x-y) 4) y(x-z) +z(z-x) 5) 27x² (y-1) -9x²(1-y) 6) 36-12x+ x² 7) 4x² + 12x+9 9) 8x ³

Đáp án:

1/ $3x^2y^2(x-2y+3)$

2/ $6y(2x^2-3xy-5y)$

3/ $(x-y)(5-y)$

4/ $(x-z)(y-z)$

5/ $18x^2(y-1)$

6/ $(x-6)^2$

7/ $(2x+3)^2$

9/ `(2x+\frac{1}{3})(4x^2+\frac{2}{3}x+\frac{1}{9})`

10/ $(5-2x-y)(5+2x+y)$

11/ $(x+y)(x+y-z)$

Giải thích các bước giải:

1/ $3x^3y^2-6x^2y^3+9x^2y^2$

$=3x^2y^2(x-2y+3)$

2/ $12x^2y-18xy^2-30y^2$

$=6y(2x^2-3xy-5y)$

3/ $5(x-y)-y(x-y)$

$=(x-y)(5-y)$

4/ $y(x-z)+z(z-x)$

$=y(x-z)-z(x-z)$

$=(x-z)(y-z)$

5/ $27x^2(y-1)-9x^2(y-1)$

$=(y-1)(27x^2-9x^2)$

$=18x^2(y-1)$

6/ $36-12x+x^2$

$=x^2-2.6x+6^2$

$=(x-6)^2$

7/ $4x^2+12x+9$

$=(2x)^2+2.2x.3+3^2$

$=(2x+3)^2$

9/ $8x^3+\dfrac{1}{27}$

$=(2x)^3+\dfrac{1}{3^3}$

`=(2x+\frac{1}{3})(4x^2+\frac{2}{3}x+\frac{1}{9})`

10/ $25-4x^2-4xy-y^2$

$=25-(4x^2+4xy+y^2)$

$=5^2-(2x+y)^2$

$=(5-2x-y)(5+2x+y)$

11/ $x^2+2xy+y^2-xz-yz$

$=(x+y)^2-z(x+y)$

$=(x+y)(x+y-z)$

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