a) Ta có: \(\left(3x-2\right)^2+2\left(3x-2\right)\left(3x+2\right)+\left(3x+2\right)^2\)

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

\(=36x^2\)(1)

Thay \(x=-\dfrac{1}{3}\) vào biểu thức (1), ta được:

\(36\cdot\left(-\dfrac{1}{3}\right)^2=36\cdot\dfrac{1}{9}=4\)

b) Sửa đề: \(\left(x+y-7\right)^2-2\cdot\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)

Ta có: \(\left(x+y-7\right)^2-2\cdot\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)

\(=\left(x+y-7-y+6\right)^2\)

\(=\left(x-1\right)^2=100^2=10000\)

a, \(A=\left(3x-2\right)^2+\left(3x+2\right)^2+2\left(9x^2-4\right)\)

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

      \(=\left(3x-2+3x+2\right)^2\)

      \(=36x^2=36.\left(-\frac{1}{3}\right)^2=4\)

b,  \(B=\left(x+y-7\right)^2-2\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)

        \(=\left[\left(x+y-7\right)-\left(y-6\right)\right]^2\)

        \(=\left(x-1\right)^2\)

        \(=\left(101-1\right)^2=10000\)

c, \(C=4x^2-20x+27\)

       \(=\left(2x\right)^2-2.2x.5+5^2+2\)

       \(=\left(2x-5\right)^2+2\)

       \(=\left(52,5.2-5\right)^2+2\)

        \(=100^2+2=10002\)

Bài này dễ mà chỉ dùng hằng đẳng thức thôi. Chúc bạn học tốt.

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

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

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

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

\(=\left(6x\right)^2\)

\(=36x^2\)

Thay: \(x=-\frac{1}{3}\) vào A ta có:

\(36.\left(-\frac{1}{3}\right)^2=36.\frac{1}{9}=4\)

b) \(B=\left(x+y-7\right)^2-2\left(x+y-7\right)\left(y-6\right)+\left(y-6\right)^2\)

\(=\left(x+y-7-y+6\right)^2\)

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

Thay x = 101 vào B ta có

\(\left(101-1\right)^2=100^2=10000\)

c) \(C=4x^2-20x+27\)

\(=\left(2x\right)^2-2.2x.5+25+2\)

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

Thay x = 52,5 vào C ta có:

\(\left(2.52,5-5\right)^2+2\)

\(=105^2+2\)

= 11027

P/s: K chắc!

Đề này đúng ra là tính nhé.

a. (3x-2)^2 +(3x+2)^2 + 2(9x^2) - 4 tại x= -1/3

Câu a sai đề nữa nè

Ta có:

\((3x-2)^2 + (3x+2)^2 + 2(9x^2-4) \)

\(= (9x^2 - 6x+4) + (9x^2+6x+4) + 2(9x^2 - 4)\)

\(= 2(9x^2+4) + 2(9x^2 -4) = 2.2.9x^2 \)

\(=36\cdot\dfrac{1}{9}=4\)

b. (x + y-7)^2 - 2(x+y -7)(y-6) + (y-6)^2 tại x= 101

Ta có:

\((x + y-7)^2 - 2(x+y -7)(y-6) + (y-6)^2\)

\(= [(x+y-7) - (y-6)]^2\)

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

\(=100^2=10000\)

c.4x^2 - 20x +27 tại 52,5

Ta có:

\(4x^2 - 20x +27\)

\(=(2x)^2 -2.2x.5 + 25 + 2 \)

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

\(=100^2+2=10002\)

mọi người trả lời giúp mình với mình cần gấp

a.\(x=0;y=-1\)

\(\Rightarrow2.0-\dfrac{-1\left(0^2-2\right)}{0.-1-1}=0-\dfrac{2}{-1}=2\)

b.\(x=2\)

\(\Rightarrow4.2^2-3\left|2\right|-2=16-6-2=8\)

\(x=-3\)

\(\Rightarrow4.\left(-3\right)^2-3\left|-3\right|-2=36-9-2=25\)

c.\(x=-\dfrac{1}{5};y=-\dfrac{3}{7}\)

\(\Rightarrow5.\left(-\dfrac{1}{5}\right)^2-7.\left(-\dfrac{3}{7}\right)+6=5.\dfrac{1}{25}+3+6=\dfrac{1}{5}+3+6=\dfrac{46}{5}\)

thay x=2 và biểu thức A ta đc

\(A=4.2^2-3.\left|2\right|-2=4.4-6-2=16-6-2=8\)

thay x=-3  biểu thức A ta đc

\(A=4.\left(-3\right)^2-3.\left|-3\right|-2=4.9-9-2=36-9-2=25\)

thay x=-1/5 ; y=-3/7  biểu thức B ta đc

\(B=5.\left(-\dfrac{1}{5}\right)^2-7.\left(-\dfrac{3}{7}\right)+6\)

\(B=5\cdot\dfrac{1}{25}+3+6\)

\(B=\dfrac{1}{5}+3+6=\dfrac{46}{5}\)

 thay x =0 , y= -1 và biểu thức ta  đc

\(0-\dfrac{\left(-1\right)\left(0^2-2\right)}{0.\left(-1\right)+\left(-1\right)}=0-\dfrac{2}{-1}=0+2=2\)

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

Thay x=-6 ; y=8 ta có:

            \(x^2+y^2=\left(-6\right)^2+8^2=36+84=100\)

b)\(x\left(x^2-y\right)-x^2\left(x-y\right)+y\left(x^2-x\right)\\ =x^3-xy-x^3+x^2y+x^2y-xy\\ =2x^2y-2xy\\ =2xy\left(x-1\right)\)

Với x=\(\frac{1}{2}\)  ; y=-100 ta có:

      \(2xy\left(x-1\right)=2\cdot\frac{1}{2}\cdot\left(-100\right)\cdot\left(\frac{1}{2}-1\right)=-100\cdot-\frac{1}{2}=50\)

Sgk trang may vay

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

Bài 1 :

a) \(M=\dfrac{1}{2}x^2y.\left(-4\right)y\)

\(\Rightarrow M=-2x^2y^2\)

Khi \(x=\sqrt[]{2};y=\sqrt[]{3}\)

\(\Rightarrow M=-2.\left(\sqrt[]{2}\right)^2.\left(\sqrt[]{3}\right)^2\)

\(\Rightarrow M=-2.2.3=-12\)

b) \(N=xy.\sqrt[]{5x^2}\)

\(\Rightarrow N=xy.\left|x\right|\sqrt[]{5}\)

\(\Rightarrow\left[{}\begin{matrix}N=xy.x\sqrt[]{5}\left(x\ge0\right)\\N=xy.\left(-x\right)\sqrt[]{5}\left(x< 0\right)\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}N=x^2y\sqrt[]{5}\left(x\ge0\right)\\N=-x^2y\sqrt[]{5}\left(x< 0\right)\end{matrix}\right.\)

Khi \(x=-2< 0;y=\sqrt[]{5}\)

\(\Rightarrow N=-x^2y\sqrt[]{5}=-\left(-2\right)^2.\sqrt[]{5}.\sqrt[]{5}=-4.5=-20\)

2:

Tổng của 4 đơn thức là;

\(A=11x^2y^3+\dfrac{10}{7}x^2y^3-\dfrac{3}{7}x^2y^3-12x^2y^3=0\)

=>Khi x=-6 và y=15 thì A=0