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![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(a^3+a^2b-a^2c-abc=a^2\left(a+b\right)-ac\left(a+b\right)=a\left(a+b\right)\left(a-c\right)\)
b) mk chỉnh lại đề
\(x^2+2xy+y^2-xz-yz=\left(x+y\right)^2-z\left(x+y\right)=\left(x+y\right)\left(x+y-z\right)\)
c) \(4-x^2-2xy-y^2=4-\left(x+y\right)^2=\left(2-x-y\right)\left(2+x+y\right)\)
d) \(x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
a.
$2x-1=0$
$2x=1$
$x=\frac{1}{2}$
b.
$\frac{3}{4}x-5=0$
$\frac{3}{4}x=5$
$x=5:\frac{3}{4}=\frac{20}{3}$
c. $x^2-4=0$
$x^2=4=2^2=(-2)^2$
$\Rightarrow x=2$ hoặc $x=-2$
d.
$x^2+3x+2=0$
$x(x+1)+2(x+1)=0$
$(x+1)(x+2)=0$
$\Rightarrow x+1=0$ hoặc $x+2=0$
$\Rightarrow x=-1$ hoặc $x=-2$
e.
$x^2+3x-4=0$
$x(x-1)+4(x-1)=0$
$(x-1)(x+4)=0$
$\Rightarrow x-1=0$ hoặc $x+4=0$
$\Rightarrow x=1$ hoặc $x=-4$
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có: \(a^3y^3+125\)
\(=\left(ay+5\right)\left(a^2y^2-5ay+25\right)\)
b) Ta có: \(8x^3-y^3-6xy\cdot\left(2x-y\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy+y^2\right)-6xy\left(2x-y\right)\)
\(=\left(2x-y\right)\left(4x^2+2xy-6xy+y^2\right)\)
\(=\left(2x-y\right)^3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(4x^4-21x^2y^2+y^4\)
\(=\left(4x^4+4x^2y^2+y^4\right)-25x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(5xy\right)^2\)
\(=\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,4x^4-21x^2y^2+y^4=\left(2x^2\right)^2+4x^2y^2+y^4-4x^2y^2-21x^2y^2\)
\(=\left(2x^2+y^2\right)^2-25x^2y^2\)
\(=\left(2x^2+y^2-5xy\right)\left(2x^2+y^2+5xy\right)\)
\(b,x^5-5x^3+4x=x\left(x^4-5x^2+4\right)\)
\(=x\left(x^4-4x^2-x^2+4\right)\)
\(=x\left[x^2\left(x^2-4\right)-\left(x^2-4\right)\right]\)
\(=x\left(x^2-4\right)\left(x^2-1\right)\)
\(=x\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)\)
\(c,x^3+5x^2+3x-9=x^3-x^2+6x^2-6x+9x-9\)
\(=x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)\)
\(=\left(x-1\right)\left(x^2+3x+3x+9\right)\)
\(=\left(x-1\right)\left[x\left(x+3\right)+3\left(x+3\right)\right]\)
\(=\left(x-1\right)\left(x+3\right)\left(x+3\right)\)
\(=\left(x-1\right)\left(x+3\right)^2\)
\(d,x^{16}+x^8-2=x^{16}+2x^8-x^8-2\)
\(=x^8\left(x^8-1\right)+2\left(x^8-1\right)\)
\(=\left(x^8-1\right)\left(x^8+2\right)\)
a) (x-1)(2x+5)
b) (x+1)(x-5)
c) [(x+1)^2](x^2+x+1)
d) (x-1)(x^3-x-1)
e) (x+y)(x-y-1)
a) 2x2 + 3x - 5 = 2x2 + 5x - 2x - 5 = x(2x + 5) - (2x + 5) = (x - 1)(2x + 5)
b) x2 - 4x - 5 = x2 - 5x + x - 5 = x(x - 5) + (x - 5) = (x + 1)(x - 5)
c) x4 + x3 + x + 1 = x3(x + 1) + (x + 1) = (x + 1)(x3 + 1) = (x + 1)2(x2 - x + 1)
d) x4 - x3 - x2 + 1 = x3(x - 1) - (x - 1)(x + 1) = (x - 1)(x3 - x - 1)
e) -x - y2 + x2 - y = -(x + y) + (x - y)(x + y) = (-1 + x - y)(x + y)