a/ \(\left(-2x^2y\right)5xy^4\)

\(=-10x^3y^5\)

tự lm tiếp, rất dễ

a) Ta có: \(\left(-2x^2y\right)\cdot\left(5xy^4\right)\)

\(=\left(-2\cdot5\right)\cdot\left(x^2\cdot x\right)\cdot\left(y\cdot y^4\right)\)

\(=-10x^3y^5\)

b) Ta có: \(\left(\dfrac{27}{10}x^4y^2\right)\cdot\left(\dfrac{5}{9}xy\right)\)

\(=\left(\dfrac{27}{10}\cdot\dfrac{5}{9}\right)\cdot\left(x^4\cdot x\right)\cdot\left(y^2\cdot y\right)\)

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

c) Ta có: \(\left(\dfrac{1}{3}x^3y\right)\cdot\left(-xy\right)^2\)

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

\(=\dfrac{1}{3}x^5y^3\)

a: \(A=\dfrac{2}{3}x^2y\cdot\dfrac{3}{4}x^4y^3=\dfrac{1}{2}x^6y^4\)

\(B=\dfrac{-1}{2}xy^2\cdot4x^5y^2=-2x^6y^4\)

b: \(C=A-B=\dfrac{-3}{2}x^6y^4\)

Bậc là 10

c: A-B nhận được giá trị âm với mọi x,y

1. \(A+7x^2y-5xy^2-xy=x^2y+8xy^2-5xy\)

\(\Rightarrow A+7x^2y-x^2y-5xy^2-8xy^2-xy+5xy=0\)

\(\Rightarrow A+6x^2y-13xy^2+4xy=0\)

\(\Rightarrow A=-6x^2y+13xy^2-4xy\)

2. \(4xy^2-7x+1-A=3x^2-7x-1\)

\(\Rightarrow4xy^2-3x^2-7x+7x+1+1-A=0\)

\(\Rightarrow4xy^2-3x^2+2-A=0\)

\(\Rightarrow A=4xy^2-3x^2+2\)

Đặt \(A=xy+x^2y^2+x^3y^3+...+x^{100}y^{100}\)

\(\Rightarrow A=xy+\left(xy\right)^2+\left(xy\right)^3+...+\left(xy\right)^{100}\)

\(\Rightarrow A=\left(-1\right)+1+\left(-1\right)+...+1\) ( 100 số hạng )

\(\Rightarrow A=\left[\left(-1\right)+1\right]+\left[\left(-1\right)+1\right]+...+\left[\left(-1\right)+1\right]\) ( 50 cặp số )

\(\Rightarrow A=0\)

Vậy A = 0

\(1,\)

\(\left(x^2-9y^2\right)\left(4x+12y\right)\)

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

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

\(3,\)

\(-x^2+2xy-y^2+25\)

\(=-\left(x^2-2xy+y^2\right)+25\)

\(=25-\left(x-y\right)^2\)

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

\(=\left(5-x+y\right)\left(5+x-y\right)\)

\(5,\)

\(x^3-6x^2+9\)

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

\(=x\left(x-3\right)^2\)

a: \(A=2a^2b-8b^2+5a^2b+5c^2-3b^3+4c^2\)

\(=7a^2b-8b^2-3b^3+c^2\)

Bậc là 3

b: \(B=7x^2y+2xy+3-2y-2x^2y+xy\)

\(=5x^2y+3xy-2y+3\)

Bậc là 3