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 + $\frac{1}{27}$
10) 25-4x ²-4xy-y ²
11) x ² + 2xy+y ²-xz-yz
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 + $\frac{1}{27}$
10) 25-4x ²-4xy-y ²
11) x ² + 2xy+y ²-xz-yz
Đáp án:
1 ,.3x³y² – 6x²y³ + 9x²y²
= 3x²y².(x – 2y + 3)
2, 12x²y – 18xy² – 30y²
= 6y(2x² – 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, 27x²(y – 1) – 9x²(1 – y)
= 27x²(y – 1) + 9x²(y – 1)
= (27x² + 9x²)(y – 1)
= 36x²(y -1)
6, 36 – 12x + x²
= x² – 2.6x + 6²
= (x – 6)²
7, 4x² + 12x + 9
= (2x)² + 2.2.3x + 3²
= (2x + 3)²
9, 8x³ + $\frac{1}{27}$
= (2x)³ + ($\frac{1}{3}$)²
= (2x + $\frac{1}{3}$ )(4x² – $\frac{2x}{3}$ + $\frac{1}{9}$ )
10, 25 – 4x² – 4xy – y²
= 25 – (4x² + 4xy + y²)
= 5² – (2x + y)²
= (5 – 2x – y)(5 + 2x + y)
11, x² + 2xy + y² – xz – yz
= (x + y)² – z(x + y)
= (x + y)(x + y – z)
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/ $x^2+2xy+y^2-xz-yz$
$=(x+y)^2-z(x+y)$
$=(x+y)(x+y-z)$