\(a,A+B-C=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-5x^3y-3x^2y^2-17y^4-1\)

\(=\left(16x^4-15x^4\right)+\left(-8x^3y+3x^3y-5x^3y\right)+\left(7x^2y^2-5x^2y^2-3x^2y^2\right)+\left(-9y^4-6y^4-17y^4\right)-1\)

\(=x^4-10x^3y-x^2y^2-32y^4-1\)

\(b,A-C+B=A+B-C\) ( giống câu a )

\(a,\)

\(A+B+C\)

\(=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-\left(5x^3y+3x^2y^2+17y^4+1\right)\)

\(=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-5x^3y-3x^2y^2-17y^4-1\)

\(=\left(16x^4-15x^4\right)+\left(-9y^4-6y^4-17y^4\right)+\left(-8x^3y+3x^3y-5x^3y\right)+\left(7x^2y^2-5x^2y^2-3x^2y^2\right)-1\)

\(=x^4-32y^4-10x^3y-x^2y^2-1\)

\(b,\)

\(A-C+B=A+B-C=x^4-32y^4-10x^3y-x^2y^2-1\)

a: A+B-C

=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4-C

=x^4-5x^3y+2x^2y^2-15y^4-5x^3y-3x^2y^2-17y^4-1

=x^4-10x^3y-x^2y^2-32y^4-1

b: A-C+B=A+B-C=x^4-10x^3y-x^2y^2-32y^4-1

Giả sử 3 đa thức trên cùng nhận giá trị âm với mọi x, y.
Ta có:     \(A.B.C\)\(=\left(16x^4-8x^3y+7x^2y^2-9y^4\right)+\left(-15x^4+3x^3y-5x^2y^2-6y^4\right)+\left(5x^3y+3x^2y^2+17y^4+1\right)\)
\(=16x^4-8x^3y+7x^2y^2-9y^4-15x^4+3x^3y-5x^2y^2-6y^4+5x^3y+3x^2y^2+17y^4+1\)
\(=\left(16x^4-15x^4\right)-\left(8x^3y-3x^3y-5x^3y\right)+\left(7x^2y^2-5x^2y^2+3x^2y^2\right)-\left(9y^4+6y^4-17y^4\right)+1\)
\(=x^4-0+5x^2y^2-2y^4+1\)
\(=x^4+5x^2y^2-2y^4+1\)

Ta thấy:        \(x^4\ge0\) \(\forall x\)   \(;\)         \(x^2y^2\ge0\)\(\forall x,y\)       \(;\)         \(y^4\ge0\)\(\forall y\)
     \(\Rightarrow\)\(\left(x^4+5x^2y^2-2y^4+1\right)\ge1\)                  \(\forall x,y\)
     \(\Rightarrow\)\(A.B.C\)nhận giá trị dương
     \(\Rightarrow\)3 đa thức trên không thể cùng nhận giá trị âm với mọi x, y 
      \(\Rightarrow\)\(dpcm\)

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

xin hỏi bạn có viết lộn không, vế trái không có Z mà tại sao vế phải lại xuất hiện Z vậy

\(=\dfrac{30\left(x^3-y^3\right)\left(x^2-y^2\right)}{3\left(x+y\right)\left(x^2+xy+y^2\right)}=\dfrac{10\left(x-y\right)^2\left(x+y\right)\left(x^2+xy+y^2\right)}{\left(x+y\right)\left(x^2+xy+y^2\right)}=10\left(x-y\right)^2\)

Nguyễn Ngọc Thanh Trúc đề là gì

thực hiện phép tính

a) \(\dfrac{25x^3y}{7z}.\dfrac{28z}{15x^2y^5}\)

\(=\dfrac{25x^3y.28z}{7z.15x^2y^5}\)

\(=\dfrac{700x^3yz}{105x^2y^5z}\)

\(=\dfrac{20x}{3y^4}\)

b) \(\dfrac{x^2+3x+9}{2x+10}.\dfrac{x+5}{x^3+27}\)

\(=\dfrac{\left(x^2+3x+9\right)\left(x+5\right)}{\left(2x+10\right)\left(x^3+27\right)}\)

\(=\dfrac{x^3+3x^2+9x+5x^2+15x+45}{2x^4+54x+10x^3+270}\)

\(=\dfrac{x^3+8x^2+24x+45}{2x^4+10x^3+54x+270}\)

ĐKXĐ: \(\left\{{}\begin{matrix}x\ne\dfrac{2}{15}\\y\ne-\dfrac{4}{9}\end{matrix}\right.\)

\(\left\{{}\begin{matrix}9y+6+20x-16=0\\\left(5x-4\right)\left(9y+4\right)=\left(3y+2\right)\left(15x-2\right)\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}20x+9y=10\\5x+15y=-6\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{4}{5}\\y=-\dfrac{2}{3}\end{matrix}\right.\)

a: =>A-B=3x^2y-4xy^2+x^2y-2xy^2=4x^2y-6xy^2

b: =>B-A=-7xy^2+8x^2y-5xy^2+6x^2y=-12xy^2+14x^2y

=>A-B=12xy^2-14x^2y

c: =>B-A=8x^2y^3-4x^3y-3x^2y^3+5x^3y^2=5x^2y^3+x^3y^2

=>A-B=-5x^2y^3-x^3y^2

d: =>A-B=2x^2y^3-7x^3y+6x^2y^3+3x^3y^2=8x^2y^3-7x^3y+3x^3y^2