a: \(70a+84b-20ab-24b^2\)

\(=\left(70a+84b\right)-\left(20ab+24b^2\right)\)

\(=14\left(5a+6b\right)-4b\left(5a+6b\right)\)

\(=\left(5a+6b\right)\left(14-4b\right)\)

\(=2\left(7-2b\right)\left(5a+6b\right)\)

b: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2\right)+\left(y^2z+yz^2\right)+3xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+3xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2\right)+yz\left(y+z\right)+2xyz+xyz\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2yz\right)+yz\left(y+z+x\right)\)

\(=x^2\left(y+z\right)+x\left(y+z\right)^2+yz\left(y+z+x\right)\)

\(=\left(y+z\right)\cdot x\left(x+y+z\right)+yz\left(y+z+x\right)\)

\(=\left(y+z+x\right)\cdot\left(xy+xz+yz\right)\)

c: \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)

\(=\left(x^2y+x^2z\right)+\left(xy^2+xz^2+2xyz\right)+\left(y^2z+yz^2\right)\)

\(=x^2\left(y+z\right)+x\left(y^2+z^2+2xz\right)+yz\left(y+z\right)\)

\(=\left(y+z\right)\left(x^2+yz\right)+x\left(y+z\right)^2\)

\(=\left(y+z\right)\left(x^2+yz+xy+xz\right)\)

\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)

\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+3xyz\)

\(=\left(x^2y+xy^2+xyz\right)+\left(y^2z+yz^2+xyz\right)+\left(x^2z+xz^2+xyz\right)\)

\(=xy\left(x+y+z\right)+yz\left(y+z+x\right)+xz\left(x+z+y\right)\)

\(=\left(x+y+z\right)\left(xy+yz+xz\right)\)

3) \(x^2\left(x+2y\right)-x-2y\)

\(=x^2\left(x+2y\right)-\left(x+2y\right)\)

\(=\left(x^2-1\right)\left(x+2y\right)\)

\(=\left(x+1\right)\left(x-1\right)\left(x+2y\right)\)

4) \(x^3-4x^2-9x+36\)

\(=\left(x^3-4x^2\right)-\left(9x-36\right)\)

\(=x^2\cdot\left(x-4\right)-9\left(x-4\right)\)

\(=\left(x-4\right)\left(x^2-9\right)\)

\(=\left(x-4\right)\left(x+3\right)\left(x-3\right)\)

\(x^2\left(x+2y\right)-x-2y\\ =x^2\left(x+2y\right)-\left(x+2y\right)\\ =\left(x^2-1\right)\left(x+2y\right)\\ =\left(x-1\right)\left(x+1\right)\left(x+2y\right)\\ ---\\ x^3-4x^2-9x+36\\ =x^2\left(x-4\right)-9\left(x-4\right)\\ =\left(x^2-9\right)\left(x-4\right)\\ =\left(x-3\right)\left(x+3\right)\left(x-4\right)\)

\(a,=\left(x-y\right)\left(x+y\right)+11\left(x-y\right)=\left(x-y\right)\left(x+y+11\right)\\ b,=\left(x+z\right)\left(x^2-xz+z^2\right)+y\left(x^2+z^2-xz\right)\\ =\left(x^2-xz+z^2\right)\left(x+y+z\right)\)

a. x² - y² + 11x - 11y

= (x + y)(x - y) + 11(x - y)

= (x + y + 11)(x - y)

b. Mik ko hiểu đề lắm

\(=xy\left(x+y\right)-7\left(x+y\right)=\left(x+y\right)\left(xy-7\right)\)

a) \(B=x^3+x^2z+y^2z-xyz+y^3\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)+z\left(x^2-xy+y^2\right)\)

\(=\left(x^2-xy+y^2\right)\left(x+y+z\right)\)

b) \(B=\left(x^2-xy+y^2\right)\left(x+y+z\right)=x^2-xy+y^2\)

\(=x^2-2.x.\dfrac{1}{2}y+\dfrac{1}{4}y^2+\dfrac{3}{4}y^2=\left(x-\dfrac{1}{2}y\right)^2+\dfrac{3}{4}y^2\ge0\)

Dấu bằng xảy ra khi \(x=y=0\)

`@` `\text {Ans}`

`\downarrow`

`a,`

`3x^2 + 6xy + 3y^2 - 3z`

`= 3*x^2 + 3*2xy + 3y^2 - 3z`

`= 3(x^2 + 2xy + y^2 - z)`

`b,`

`x^3 + x^2y - x^2z - xyz`

`= x(x + y)(x-z)`