a: \(x^{n}\cdot y^{n+2}\left(xy+x^2y+1\right)\)

\(=x^{n}\cdot y^{n+2}\cdot xy+x^{n}\cdot y^{n+2}\cdot x^2y+x^{n}y^{n+2}\)

\(=x^{n+1}\cdot y^{n+3}+x^{n+2}\cdot y^{n+3}+x^{n}y^{n+2}\)

b: \(\left(4x^{n-2}+x^{n+1}\right)\cdot x^{n}\)

\(=4x^{n-2}\cdot x^{n}+x^{n+1}\cdot x^{n}\)

\(=4x^{2n-2}+x^{2n+1}\)

c: \(4xy\left(x^{n-2}y^{n+1}+x^{n}y^{n+1}\right)\)

\(=4xy\cdot x^{n-2}\cdot y^{n+1}+4xy\cdot x^{n}y^{n+1}\)

\(=4x^{n-1}y^{n+2}+4x^{n+1}\cdot y^{n+2}\)

\(4xy\left(x^{n-2}y^{n+1}+x^{n}y^{n+1}\right)\)

\(=4xy\cdot x^{n-2}\cdot y^{n+1}+4xy\cdot x^{n}y^{n+1}\)

\(=4x^{n-1}y^{n+2}+4x^{n+1}\cdot y^{n+2}\)

4x\(^{1+n-2}\)y\(^{1+n+1}\)4xy\(^{1+n}\)+4xy

Sửa đề: \(4xy\left(x^{n-2}y^{n+1}+x^{n}\cdot y^{n+1}\right)\)

\(4xy\left(x^{n-2}y^{n+1}+x^{n}y^{n+1}\right)\)

\(=4xy\cdot x^{n-2}\cdot y^{n+1}+4xy\cdot x^{n}y^{n+1}\)

\(=4x^{n-1}y^{n+2}+4x^{n+1}\cdot y^{n+2}\)

x²y + xy² - x - y

= (x²y + xy²) - (x + y)

= xy(x + y) - (x + y)

= (x + y)(xy - 1)

a) \(3x\left(5x^2-2x-1\right)\)

\(=3x.5x^2-3x.2x+3x.\left(-1\right)\)

\(=15x^3-6x^2-3x\)

b) \(\left(x^3-2xy+3\right)\left(-xy\right)\)

\(=\left(-xy\right).\left(x^2+2xy-3\right)\)

\(=\left(-xy\right).x^2+\left(-xy\right).2xy+\left(-xy\right).\left(-3\right)\)

\(=x^3y-2x^2y^2+3xy\)

mấy câu sau vt lại đè

          c)x²y(2x³ - xy² - 1);

          d)x(1,4x - 3,5y);

          e)xy(x² - xy + y²);

          f)(1 + 2x - x2)5x;

          g) (x²y - xy + xy² + y³). 3xy²;  

          h) x²y(15x - 0,9y + 6);

Đây ạ giúp mik vs bt tết đs mng :<

Làm tính nhân:

a. 3 x(5x2 - 2x -1) = 15x3 - 6x2 - 3x

b. (x2+2xy -3)(-xy) = - x3y – 2x2y2 + 3xy

c. 1/2 x2y ( 2x3 - 2/5 xy2 -1 )= x5y - 1/5 x3y3 - 1/2 x2y

f: \(4x^4+1\)

\(=4x^4+4x^2+1-4x^2\)

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

e: \(x^2y-xy^2+x^3-y^3\)

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

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

d: \(\left(xy+ab\right)^2+\left(ay-bx\right)^2\)

\(=x^2y^2+a^2b^2+2\cdot ab\cdot xy+a^2y^2-2\cdot ay\cdot bx+b^2x^2\)

\(=x^2y^2+a^2y^2+a^2b^2+_{}x^2b^2\)

\(=y^2\left(a^2+x^2\right)+b^2\left(a^2+x^2\right)=\left(a^2+x^2\right)\left(y^2+b^2\right)\)

c: \(a\left(x^2+4\right)-x\left(a^2+4\right)\)

\(=a\cdot x^2-x\cdot a^2+4a-4x\)

=ax(x-a)+4(a-x)

=(x-a)(ax-4)

b: \(m^3p+m^2np-m^2p^2-mnp^2\)

\(=mp\left(m^2+mn-mp-np\right)\)

=mp[m(m+n)-p(m+n)]

=mp(m+n)(m-p)

a: \(2x-72x^3=2x\cdot1-2x\cdot36x^2=2x\left(1-36x^2\right)\)

=2x(1-6x)(1+6x)

a) \(4\left(2-x\right)^2+xy-2y\)

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

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

\(=\left(x-2\right)\left(4x-8\right)+y\left(x-2\right)\)

\(=\left(x-2\right)\left(4x-8+x-2\right)\)

\(=\left(x-2\right)\left(5x-10\right)\)

\(=5\left(x-2\right)^2\)

a, \(=4\left(x-2\right)^2+y\left(x-2\right)=\left(x-2\right)\left(4x-8+y\right)\)

b, \(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-xy+y^2-y^2\right]=\left(x-y\right)\left(x^3-2x^2y+xy^2-xy\right)=x\left(x-y\right)\left(x^2-2xy+y^2-y\right)\)

c, \(=xy\left(x-y\right)-3\left(x-y\right)=\left(xy-3\right)\left(x-y\right)\)

d, không phân tích được