Bài 3: Những hằng đẳng thức đáng nhớ
Các câu hỏi tương tự
Bài 1 :Tìm x,y ,biết :
a) \(\left(3x-1\right)^2-\left(3x+2\right)\left(3x-2\right)=2014\)
b) \(5x^2+4xy+4y^2+4x+1=0\)
Bài 2 : Chứng minh rằng các biểu thức sau không phụ thuộc vào các biến x,y:
D = \(\left(2x-3y\right)^2-\left(3y-2\right)\left(3y+2\right)-\left(1-2x\right)^2+4x\left(3y-1\right)\)
Bài 1 :
a) left(6x^2+frac{1}{3}right)^2
b) left(5x-4yright)^2
c) left(2x^2y-3y^2xright)^2
d) left(5x-3right).left(5x+3right)
e) left(-4xy-5right).left(5-4xyright)
f) left(a^2b+ab^2right).left(ab^2-a^2bright)
g) left(3x-4right)^2+2.left(3x-4right).left(4-xright)+left(4-xright)^2
h) left(a^2+ab+b^2right).left(a^2-ab+b^2right)-left(a^4+b^4right)
Đọc tiếp
Bài 1 :
a) \(\left(6x^2+\frac{1}{3}\right)^2\)
b) \(\left(5x-4y\right)^2\)
c) \(\left(2x^2y-3y^2x\right)^2\)
d) \(\left(5x-3\right).\left(5x+3\right)\)
e) \(\left(-4xy-5\right).\left(5-4xy\right)\)
f) \(\left(a^2b+ab^2\right).\left(ab^2-a^2b\right)\)
g) \(\left(3x-4\right)^2+2.\left(3x-4\right).\left(4-x\right)+\left(4-x\right)^2\)
h) \(\left(a^2+ab+b^2\right).\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)
Thực hiện phép tính :
a, \(\left(x^2+\dfrac{2}{5}y\right)\cdot\left(x^2-\dfrac{2}{5}y\right)\)
b,\(\left(3x-2y\right)\cdot\left(3x+2y\right)\cdot\left(9x^2+4y^2\right)\)
Tính
a/ left(x-3right)left(x^2+3x+9right)
b/ left(x-2right)left(x^2+2x+4right)
c/ left(x+4right)left(x^2-4x+16right)
d/ left(x-3yright)left(x^2+3xy+9y^2right)
e/ left(x^2-frac{1}{3}right)left(x^4+frac{1}{3}x^2+frac{1}{9}right)
f/ left(frac{1}{3}x+2yright)left(frac{1}{9}x^2-frac{2}{3}xy+4y^2right)
Đọc tiếp
Tính
a/ \(\left(x-3\right)\left(x^2+3x+9\right)\)
b/ \(\left(x-2\right)\left(x^2+2x+4\right)\)
c/ \(\left(x+4\right)\left(x^2-4x+16\right)\)
d/ \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)
e/ \(\left(x^2-\frac{1}{3}\right)\left(x^4+\frac{1}{3}x^2+\frac{1}{9}\right)\)
f/ \(\left(\frac{1}{3}x+2y\right)\left(\frac{1}{9}x^2-\frac{2}{3}xy+4y^2\right)\)
Tìm x:
1,left(3x-5right)^2-left(3x+1right)^28
2,2x.left(8x-3right)-left(4x-3right)^227
3,left(2x-3right)^2-left(2x+1right)^23
4, left(x+5right)^2-x^245
5, left(x-3right)^3-left(x-3right).left(x^2+3x+9right)+9.left(x+1right)^218
6,x.left(x-4right).left(x+4right)-left(x-5right).left(x^2+5x+25right)13
Đọc tiếp
Tìm x:
\(1,\left(3x-5\right)^2-\left(3x+1\right)^2=8\)
2,\(2x.\left(8x-3\right)-\left(4x-3\right)^2=27\)
3,\(\left(2x-3\right)^2-\left(2x+1\right)^2=3\)
4, \(\left(x+5\right)^2-x^2=45\)
5, \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=18\)
6,\(x.\left(x-4\right).\left(x+4\right)-\left(x-5\right).\left(x^2+5x+25\right)=13\)
Chứng minh:
a) \(\left(a-b\right)^3=-\left(b-a\right)^3\)
b) \(\left(-a-b\right)^2=\left(a+b\right)^2\)
c) \(\left(x+y\right)^3=x\left(x-3y\right)^2+y\left(y-3x\right)^2\)
d) \(\left(x+y\right)^3-\left(x-y\right)^3=2y\left(y^2+3x^2\right)\)
Rút gọn biểu thức:
a) Aleft(x-yright)^3+left(y+xright)^3+left(y-xright)^3-3xyleft(x+yright)
b) B3x^2left(x+1right)left(x-1right)-left(x^2-1right)left(x^4+x^2+1right)+left(x^2-1right)^3
c) Cleft(x+yright)left(x^2-xy+y^2right)+left(x-yright)left(x^2+xy+y^2right)-2x^3
d) Dleft(x+1right)^3+left(x-1right)^3+x^3-3xleft(x+1right)left(x-1right)
Đọc tiếp
Rút gọn biểu thức:
a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)
c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)
d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
* Tìm x :
a, \(\left(3x-2\right)^2-\left(3x-5\right).\left(3x+2\right)=11\)
b, \(\left(4x-3\right)^2-\left(4x-5\right).\left(4x+5\right)=32\)
c, \(\left(5x-2\right)^2-\left(5x+3\right).\left(5x-5\right)=1\)
d, \(\left(x-4\right)^2-\left(x-7\right).\left(2x-3\right)=5-x^2\)
Viết các biểu thức sau dưới dạng bình phương của một tổng hoặc hiệu
f) 2xy^2+x^2y^2+1
g) left(3x-2yright)^2+2left(3x-2yright)+1
h) 16-8left(x-3yright)+left(x-3yright)^2
i) 2left(x-yright)left(x+yright)+left(x+yright)^2+left(x-yright)^2
j) left(x+y-zright)^2+left(y-zright)^2+2left(x+y-zright)left(z-yright)
Đọc tiếp
Viết các biểu thức sau dưới dạng bình phương của một tổng hoặc hiệu
f) \(2xy^2+x^2y^2+1\)
g) \(\left(3x-2y\right)^2+2\left(3x-2y\right)+1\)
h) \(16-8\left(x-3y\right)+\left(x-3y\right)^2\)
i) \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
j) \(\left(x+y-z\right)^2+\left(y-z\right)^2+2\left(x+y-z\right)\left(z-y\right)\)