Bài 3:

3: \(6x\left(x-y\right)-9y^2+9xy\)

\(=6x\left(x-y\right)+9xy-9y^2\)

\(=6x\left(x-y\right)+9y\left(x-y\right)\)

\(=\left(x-y\right)\left(6x+9y\right)\)

\(=3\left(2x+3y\right)\left(x-y\right)\)

Bài 4:

sau bạn đăng tách ra cho mn cùng giúp nhé 

a, \(\left(-2x^5+3x^2-4x^3\right):2x^2=-x^3+\frac{3}{2}-2x\)

b, \(\left(x^3-2x^2y+3xy^2\right):\left(-\frac{1}{2}x\right)=-\frac{x^2}{2}+xy-\frac{3y^2}{2}\)

c, \(\left(3x^2y^2+6x^3y^3-12xy^2\right):3xy=xy+2x^2y^2-4y\)

d, \(\left(4x^3-3x^2y+5xy^2\right):\frac{1}{2}x=2x^2-\frac{3xy}{2}+\frac{5y^2}{2}\)

e, \(\left(18x^3y^5-9x^2y^2+6xy^2\right):3xy^2=6x^2y^3-3x+2\)

f, \(\left(x^4+2x^2y^2+y^4\right):\left(x^2+y^2\right)=\left(x^2+y^2\right)^2:\left(x^2+y^2\right)=x^2+y^2\)

Đáp án:

 $a.3x³-5x²+7x$

$b.-4x²y-10x²y+2xy$

$c.-x³+2x²+29x+20$

$d.2x⁴-3x³+2x²+3x-4$

$e.x²-4y²$

$h.2x²-6x+13$

$g.3xy⁴-\frac{1}{2}y²+2x²y$ 

$f.-2x²y³+y-3$

Giải thích các bước giải:

 $a.3x.(x²-5x+7)$

$=3x³-5x²+7x$

$b.-2xy.(2x³+5x-1)$

$=-4x⁴y-10xy²+2xy$

$c.(x+4).(-x²+6x+5)$

$=-x³+6x²+5x-4x²+24x+20$

$=-x³+2x²+29x+20$

$d.(x²-1).(2x²-3x+4)$

$=2x⁴-3x³+4x²-2x²+3x-4$

$=2x⁴-3x³+2x2+3x-4$

$e.(x+2y).(x-2y)$

$=x²-\left(2y\right)²$

$=x²-4y²$

$h.(3x-1)²-7(x²+2)$

$=9x²-6x+1-7x²-14$

$=2x²-6x+13$

$g.(6x²$y⁵$-xy³+4x³y²):2xy$

$=3xy⁴-\frac{1}{2}y²+2x²y$ 

$f.(-12x³y⁴+6xy²-18xy):6xy$

$=-2x³y³+y-3$

a, \(=12x^5+9x^3y^2-6x^2y^3-20x^4y-15x^2y^3-10xy^4-24x^3y^2-18xy^4+12y^5\)

(tự rút gọn cái :P)

b, \(8x^3+4x^2y-2xy^2-y^3\)

\(=4x^2\left(2x+y\right)-y^2\left(2x+y\right)=\left(2x+y\right)^2\left(2x-y\right)\)

\(4x^2y^2-4x^2-4xy-y^2=4x^2y^2-\left(2x+y\right)^2\)

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

Mấy cái còn lại nhân tung ra là được mà :))))

làm luôn đi cậu

Giúp với mọi người

c: \(=3x^3-4x^2+6x^2-8x=3x^2+2x^2-8x\)

Bài 1: 

a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)

= \(x^2\) -  16 - 5\(x\) - 5 + \(x^2\) + \(x\) 

= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)

= 2\(x^2\) - 4\(x\) - 21

b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)

=  3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7

= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)

= - 3\(x^2\) + 3\(xy\) - 3

b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)

\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)

\(=\dfrac{2y^2+8y+12}{y-1}\)

\(a,x^3\left(3x^2-x-\dfrac{1}{2}\right)\)

\(=3x^5-x^4-\dfrac{1}{2}x^3\)

\(b,\left(5xy-x^2+y\right).\dfrac{2}{5xy^2}\)

\(=\dfrac{2}{y}-\dfrac{2x}{5y^2}+\dfrac{2}{xy}\)

\(c,\left(4x^3-3xy^2+2xy\right)\left(-\dfrac{1}{3}x^2y\right)\)

\(=-\dfrac{4x^5y}{3}+x^3y^3-\dfrac{2x^3y^2}{3}\)

a/ (x-1)²-(4x+3)(2-x)=x²-2x+1-(8x-4x²+6-3x)

=x²-2x+1-8x+4x²-6+3x=5x²-7x-6

b/ (15x³y² - 6x²y³) : 3x²y² = 5x - 2y

c/ \(\dfrac{x+7}{x-7}-\dfrac{x-7}{x+7}+\dfrac{4x^2}{x^2-49}\)=\(\dfrac{\left(x+7\right)^2-\left(x-7\right)^2+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{x^2+14x+49-\left(x^2-14x+49\right)+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{28x+4x^2}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{4x\left(x+7\right)}{\left(x-7\right)\left(x+7\right)}\)=\(\dfrac{4x}{x-7}\)