Chọn câu sai: x^2 + y^2 bằng:
A.(x+y)^2 B.(x - y)^2 +2xy C.(x + y)^2 - 2xy D.y^2 + x^2
Chọn đáp án đúng
\({ (x^{3}+3x^{2}y+3xy^{2}+y^{3}-z^{3}):(x+y-z) }\)
\(A. { x^{2}+y^{2}+z^{2}+2xy+xz+yz }\)
\(B. { x^{2}+y^{2}+z^{2}+2xy-xz-yz } \)
\(D. { x^{2}+y^{2}-z^{2}+2xy-xz-yz } \)
\(\left(x^3+3x^2y+3xy^2+y^3-z^3\right):\left(x+y-z\right)\\ =\left[\left(x+y\right)^3-z^3\right]:\left(x+y-z\right)\\ =\left(x+y-z\right)\left[\left(x+y\right)^2+z\left(x+y\right)+z^2\right]:\left(x+y-z\right)\\ =x^2+2xy+y^2+xz+yz+z^2\)
Vậy chọn A
Kết quả của phép nhân \((x + y - 1)(x + y + 1)\) là:
A. \({x^2} - 2xy + {y^2} + 1\)
B. \({x^2} + 2xy + {y^2} - 1\)
C. \({x^2} - 2xy + {y^2} - 1\)
D. \({x^2} + 2xy + {y^2} + 1\)
\(\left(x+y-1\right)\left(x+y+1\right)=x^2+xy-x+xy+y^2-y+x+y-1\\ =x^2+\left(xy+xy\right)+\left(-x+x\right)+y^2+\left(-y+y\right)-1\\ =x^2+2xy+y^2-1\\ =>B\)
Cho (A):
16 x 4 ( x – y ) – x + y = ( 2 x – 1 ) ( 2 x + 1 ) ( 4 x + 1 ) 2 ( x + y )
và (B): 2 x 3 y – 2 x y 3 – 4 x y 2 – 2 x y
= 2xy(x + y – 1)(x – y + 1). Chọn câu đúng.
A. (A) đúng, (B) sai
B. (A) sai, (B) đúng
C. (A), (B) đều sai
D. (A), (B) đều đúng
Ta có
(A):
16 x 4 ( x – y ) – x + y = 16 x 4 ( x – y ) – ( x – y ) = ( 16 x 4 – 1 ) ( x – y ) = [ ( 2 x ) 4 – 1 ] ( x – y ) = [ ( 2 x ) 2 – 1 ] [ ( 2 x ) 2 + 1 ] ( x – y ) = ( 2 x – 1 ) ( 2 x + 1 ) ( 4 x 2 + 1 ) ( x – y )
Nên (A) sai
Và (B):
2 x 3 y – 2 x y 3 – 4 x y 2 – 2 x y = 2 x y ( x 2 – y 2 – 2 y – 1 ) = 2 x y [ x 2 – ( y 2 + 2 y + 1 ) ] = 2 x y [ x 2 – ( y + 1 ) 2 ] = 2 x y ( x – y – 1 ) ( x + y + 1 ) .
Nên (B) sai.
Vậy cả (A) và (B) đều sai.
Đáp án cần chọn là: C
Chứng minh (x+y)(x+y)=x^2+2xy+y^2 b(x-y)(x-y)=x^2-2xy+y^2 c(x-z)(x+z)=x^2-z^2
\(\left(x+y\right)\left(x+y\right)=x^2+xy+xy+y^2=x^2+2xy+y^2\)
\(\left(x-y\right)\left(x-y\right)=x^2-xy-xy+y^2=x^2-2xy+y^2\)
\(\left(x-z\right)\left(x+z\right)=x^2+xz-xz-z^2=x^2-z^2\)
Tìm x, y thuộc Z để:
a) xy + x - y = 2
b) x - 2xy + y = 0
c) x. (x - 2) - (2 - x)y - 2. (x - 2) = 3
d) (2x - y). (4x2 + 2xy + y2) + (2x + y). (4x2 - 2xy + y2) - 16x. (x2 - y) = 32
e) x2 - 2xy + 2y2 - 2x + 6y +5 = 0
g) x2 + 2xy + 7x + 7y + 2y2 = 0
Thực hiện phép tính:
a/(x^2+y^2-2xy)+(x^2+y^2 +2xy)
b/(x^2+y^2-2xy) - (x^2+y^2+2xy)
a.
(x^2 + y^2 - 2xy) + (x^2 + y^2 + 2xy)
= x^2 + y^2 - 2xy + x^2 + y^2 + 2xy
= (x^2 + x^2) + (y^2 + y^2) + (2xy - 2xy)
= 2x^2 + 2y^2
b.
(x^2 + y^2 - 2xy) - (x^2 + y^2 + 2xy)
= x^2 + y^2 - 2xy - x^2 - y^2 - 2xy
= (x^2 - x^2) + (y^2 - y^2) - (2xy + 2xy)
= -4xy
a) ( x+3 ) * ( x^2 - 3x +9 ) - ( 54+ x^3 )
b) ( 2x + y ) * ( 4x^2 - 2xy + y^2 ) - ( 2x - y ) * ( 4x^2 + 2xy + y^2 )
c) ( a+b ) ^3 - ( a-b ) ^3 - 2b^3
d) ( x+y+z ) ^ 2 - 2 * ( x+y+z ) * ( x+y ) + y^2 + ( x + y ) ^ 2
a) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
\(=x^3+27-54-x^3\)
\(=-27\)
b) \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=\left(8x^3+y^3\right)-\left(8x^3-y^3\right)\)
\(=8x^3+y^3-8x^3+y^3\)
\(=2y^3\)
c) \(\left(a+b\right)^3-\left(a-b\right)^3-2b^3\)
\(=\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)-\left(a-b\right)^2\right]-2b^3\)
\(=\left(a+b-a+b\right)\left[\left(a^2+2ab+b^2\right)+\left(a^2-ab+ab-b^2\right)-\left(a^2-2ab+b^2\right)\right]-2b^3\)
\(=b^2\left(a^2+2ab+b^2+a^2-ab+ab-b^2-a^2+2ab-b^2\right)-2b^3\)
....
Rút gọn biểu thức:
a) (x+y)2- (x-y)^2
b) 2*(x+y)(x-y) + (x+y)^2+(x-y)^2
c) (x+3)(x^2 -3x * 9 )(54 +x^3)
d) (2x+y)(4x^2 - 2xy + y^2 ) - (2x-y)(ax^2 +2xy +y^2 )
a) (x+y+x_y).(x+y_x+y)
b ) (( x + y )+(x _ y))2
d ) 8x3 + y3 _ 8x3 + y3 =2y3