a) \(\left(2x^3-y^2\right)^3\)

\(=\left(2x^3\right)^3-3\cdot\left(2x^3\right)^2\cdot y^2+3\cdot2x^3\cdot\left(y^2\right)^{^2}-\left(y^2\right)^3\)

\(=8x^9-3\cdot4x^6y^2+3\cdot2x^3y^4-y^6\)

\(=8x^9-12x^6y^2+6x^3y^4-y^6\)

b) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

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

\(=x^3-27y^3\)

c) \(\left(x+2y+z\right)\left(x+2y-z\right)\)

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

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

d) \(\left(2x^3y-0,5x^2\right)^3\)

\(=\left(2x^3y-\dfrac{1}{2}x^2\right)^3\)

\(=8x^9y^3-6x^8y^2+\dfrac{3}{2}x^7y-\dfrac{1}{8}x^6\)

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

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

\(=4x^4+9x^2-12x^2-27\)

\(=4x^4-3x^2-27\)

f) \(\left(2x-1\right)\left(4x^2+2x+1\right)\)

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

\(=8x^3-1\)

\(a,\left(2x^3-y^2\right)^3=8x^9-12x^6y^2+6x^3y^4-y^6\)\(b,\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-27y^3\)

\(c,\left(x+2y+z\right)\left(x+2y-z\right)=\left(x+2y\right)^2-z^2=x^2+4xy+4y^2-z^2\)\(d,\left(2x^3y-0,5x^2\right)^3=8x^9y^3-6x^4y^2x^2+3x^3yx^4-0,125x^6=8x^9y^3-6x^6y^2+3x^7y-0,125x^6\)

Gọi diện tích hình vuông là Shv.Khi đó mỗi ô vuông nhỏ có diện tích là Shv9 . Ta thấy ngay diện tích tam giác ABK bằng một nửa diện tích hình chữ nhật AKBH và bằng Shv9 .

Tương tự SAID=SDNC=SBMC=SABK=Shv9  và SIKMN=Shv9 

Vậy thì SABCD=4.Shv9 +Shv9 =59 Shv

Vậy diện tích phần còn lại bằng 49 Shv

Suy ra diện tích hình vuông ABCD bằng 54  diện tích phần còn lại.

k mình nha

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

b) \(\left(3x-\frac{1}{8}y\right)^2=9x^2-\frac{3}{4}xy+\frac{1}{64}y^2\)

c) \(\left(-6x-\frac{2}{5}\right)^2=36x^2+\frac{24}{5}x+\frac{4}{25}\)

d) \(\left(xy^2+1\right)\left(xy^2-1\right)=x^2y^4-1\)

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

f) \(\left(\frac{1}{2}x-\frac{1}{3}y-1\right)^2=\frac{1}{4}x^2+\frac{1}{9}y^2+1-\frac{1}{3}xy-x+\frac{2}{3}y\)

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

b, \(\left(3x-\frac{1}{8}y\right)^2=9x^2-\frac{3}{4}xy+\frac{1}{64}y^2\)

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

                                   Bài làm :

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

b) \(\left(3x-\frac{1}{8}y\right)^2=9x^2-\frac{3}{4}xy+\frac{1}{64}y^2\)

c) \(\left(-6x-\frac{2}{5}\right)^2=36x^2+\frac{24}{5}x+\frac{4}{25}\)

d) \(\left(xy^2+1\right)\left(xy^2-1\right)=x^2y^4-1\)

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

f) \(\left(\frac{1}{2}x-\frac{1}{3}y-1\right)^2=\frac{1}{4}x^2+\frac{1}{9}y^2+1-\frac{1}{3}xy-x+\frac{2}{3}y\)

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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

b. \(\left(5-x^2\right)\left(5+x^2\right)=25+5x^2-5x^2-x^4=-x^4+25\)

c. \(\left(2x-y\right)\left(4x^2+2xy+y^2\right)=8x^3+4x^2y+2xy^2-4x^2y-2xy^2-y^3\)

\(=8x^3-y^3\)

d. \(\left(5-3x\right)^2=25-30x+9x^2\)

e. \(\left(5x-1\right)^3=125x^3-75x^3+15x-1\)

f. \(\left(x+3\right)\left(x^2-3x+9\right)=x^3-3x^2+9x+3x^2-9x+27=x^3+27\)

h. \(\left(2x^2+3y\right)^2=4x^4+12x^2y+9y^2\)

a) (2+xy)² = 2²+4xy+(xy)² = 4 + 4xy +x²y²

b)  ( 5 - x^2 ) . ( 5 + x^2 ) = 5²-x⁴=25-x⁴

c) ( 2x - y ) . ( 4x^2 + 2xy + y^2 )  = 8x³-y³

d)(5-3x)²=5²-2.5.3x+9x²=25-30x+9x²

e) (5x-1)³=(5x)³-3.(5x)².1+3.5x.1-1 =125x³-75x²+15x-1

f) (x+3)(x²-3x+9)=(x+3)(x²-3x+3²)=x³+27

g) -x³+3x²-3x+1 =(−x+1)(x−1)(x−1)= -(x-1)³

h) (2x²+3y)²=4x⁴+2.2x².3y+9y²=4x⁴+12x²y+9y²

a)  \(x^2+4x+4=\left(x+2\right)^2\)

b)  \(9x^2-12x+4=\left(3x-2\right)^2\)

c)  \(x^2+x+\frac{1}{4}=\left(x+\frac{1}{2}\right)^2\)

d)  kiểm tra lại đề nhé

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

f)  \(9y^2-\frac{1}{4}=\left(3y-\frac{1}{2}\right)\left(3y+\frac{1}{2}\right)\)

g)  \(8x^3+8a^3=\left(2x+2a\right)\left(4x^2-4ax+4a^2\right)\)

h)  \(64x^3-27y^3=\left(4x-3y\right)\left(9y^2+12xy+16x^2\right)\)

Cảm ơn bạn nhìu !!

Ta có:

D=2x2+3y2+4xy−8x−2y+18C=2x2+3y2+4xy−8x−2y+18

D=2(x2+2xy+y2)+y2−8x−2y+18C=2(x2+2xy+y2)+y2−8x−2y+18

D=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1C=2[(x+y)2−4(x+y)+4]+(y2+6y+9)+1

D=2(x+y−2)2+(y+3)2+1≥1C=2(x+y−2)2+(y+3)2+1≥1

Dấu "=" xảy ra ⇔x+y=2⇔x+y=2và y=−3y=−3

Hay x = 5 , y = -3

Đc chx bạn