M=x2/(x+y)(1-y) - y2/(x+y)(1+x) - x2y2/(1+x)(x+y)
a. rút gọn M
b. TÌM CẶP (X;Y) để M= -6
rút gọn P=2/x-(x2/(x2-xy)+(x2-y2)/xy-y2/(y2-xy)):(x2-xy+y2)/(x-y)
r tìm gt P với |2x-1|=1 ; |y+1|=1/2
Bạn cần viết đề bằng công thức toán để được hỗ trợ tốt hơn.
Bài 3:
b) Rút gọn biểu thức B=(x+y)(2x-y)+(xy4-x2y2):xy2
Bài 4: Phân tích thành nhân tử
a) 25x3-10x2+xx
b) x2-9x+9y-y2
c) 16-x2-4y2-4xy
Bài 5: Tìm x biết
a) 36-x3=00
b) (x+2)(x-2)-(x+1)2=7
Bài 3:
b. $B=(x+y)(2x-y)+(xy^4-x^2y^2):(xy^2)$
$=(2x^2-xy+2xy-y^2)+(y^2-x)$
$=2x^2+xy-y^2+y^2-x=2x^2+xy-x$
Bài 4:
a. $25x^3-10x^2+x=x(25x^2-10x+1)=x(5x-1)^2$
b. $x^2-9x+9y-y^2=(x^2-y^2)-(9x-9y)=(x-y)(x+y)-9(x-y)=(x-y)(x+y-9)$
c. $16-x^2-4y^2-4xy=16-(x^2+4y^2+4xy)$
$=4^2-(x+2y)^2=(4-x-2y)(4+x+2y)$
Bài 5:
a. $36-x^3=100$
$x^3=36-100=-64=(-4)^3$
$\Rightarrow x=-4$
b.
$(x+2)(x-2)-(x+1)^2=7$
$\Leftrightarrow (x^2-4)-(x^2+2x+1)=7$
$\Leftrightarrow -2x-5=7$
$\Leftrightarrow -2x=12$
$\Leftrightarrow x=-6$
Bài 10 : Rút gọn các biểu thức
a. A = ( x + 2 ) ( x2 - 2x + 4 ) - x3 + 2
b . B = ( x - 1 ) ( x2 + x + 1 ) - ( x + 1 ) ( x2 - x + 1 )
c. C = ( 2x - y ) ( 4x2 + 2xy + y2 ) + ( y - 3x ) ( y2 + 3xy + 9x2 )
a) \(A=\left(x+2\right)\left(x^2-2x+4\right)-x^3+2\)
\(A=x^3+8-x^3+2\)
\(A=10\)
b) \(B=\left(x-1\right)\left(x^2+x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)
\(B=x^3-1-\left(x^3+1\right)\)
\(B=x^3-1-x^3-1\)
\(B=-2\)
c) \(C=\left(2x-y\right)\left(4x^2+2xy+y^2\right)+\left(y-3x\right)\left(y^2+3xy+9x^2\right)\)
\(C=\left(2x\right)^3-y^3+y^3-\left(3x\right)^3\)
\(C=8x^3-y^3+y^3-27x^3\)
\(C=-19x^3\)
a)
\(A=\left(x+2\right)\left(x-2\right)\left(x-2\right)-x^3+2\\ =\left(x^2-4\right)\left(x-2\right)-x^3+2\\ =x^3-2x^2-4x+8-x^3+2\\ =-2x^2-4x+10\)
b)
\(B=x^3-1-\left(x^3+1\right)\\ =x^3-1-x^3-1\\ =-2\)
c)
\(C=\left(2x\right)^3-y^3+\left(y\right)^3-\left(3x\right)^3\\ =8x^3-y^3+y^3-27x^3\\ =-19x^3\)
Bài 13 : tính nhanh
a. 5012
b . 882 + 24 . 88 + 122
c. 52 . 48
Bài 14 : rút gọn biểu thức
a. P = ( 2x - 1 ) ( 4x2 + 2x + 1 ) + ( x + 1 ) ( x2 - x + 1 )
b. Q = ( x - y ) ( x2 + xy + y2 ) - ( x + y ) ( x2 - xy + y2 ) + 2y3
Bài 13:
a) \(501^2\)
\(=\left(500+1\right)^2\)
\(=500^2+2\cdot500\cdot1+1^2\)
\(=250000+1000+1\)
\(=251001\)
b) \(88^2+24\cdot88+12^2\)
\(=88^2+2\cdot12\cdot88+12^2\)
\(=\left(88+12\right)^2\)
\(=100^2\)
\(=10000\)
c) \(52\cdot48\)
\(=\left(50+2\right)\left(50-2\right)\)
\(=50^2-2^2\)
\(=2500-4\)
\(=2496\)
Bài 14:
a) \(P=\left(2x-1\right)\left(4x^2+2x+1\right)+\left(x+1\right)\left(x^2-x+1\right)\)
\(P=\left(2x\right)^3-1+x^3+1\)
\(P=8x^3+x^3\)
\(P=9x^3\)
b) \(Q=\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x+y\right)\left(x^2-xy+y^2\right)+2y^3\)
\(Q=x^3-y^3-x^3-y^3+2y^3\)
\(Q=-2y^3+2y^3\)
\(Q=0\)
Bài `14`
`a. P = ( 2x - 1 ) ( 4x^2 + 2x + 1 ) + ( x + 1 ) ( x^2 -x+1)`
`=(2x)^3-1^3 + x^3+1^3`
`=8x^3-1+x^3+1`
`= 9x^3`
__
`b, Q = ( x - y ) ( x^2 + xy + y^2 ) - ( x + y ) ( x^2 - xy + y^2)+2y^3`
`=x^3-y^3 -(x^3+y^3)+2y^3`
`=x^3-y^3 -x^3-y^3+2y^3`
`= 0`
giúp với ạ
Bài 1:Rút gọn biểu thức
a)A=(x+y)2 - (x-y)2
b)B=(x+y)2 - 2(x+y)(x-y)+(x-y)2
c)(x2 + x +1)(x2 -x+1)(x2 -1)
d)(a+b-c)2 + (a-b+c)2 - 2(b-c)2
Bài 2: Cho các số thực x,y thỏa mãn điều kiện x+y=3; x2 +y2 =17. Tính giá trị biểu thức x3 +y3
B1
a, \(=>A=\left(x+y+x-y\right)\left(x+y-x+y\right)=2x.2y=4xy\)
b, \(=>B=\left[\left(x+y\right)-\left(x-y\right)\right]^2=\left[x+y-x+y\right]^2=\left[2y\right]^2=4y^2\)
c,\(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)
\(=\)\(\left(x+1\right)\left(x^2-x+1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x^3+1^3\right)\left(x^3-1^3\right)=x^6-1\)
d, \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
\(=\left(a+b-c\right)^2-\left(b-c\right)^2+\left(a-b+c\right)^2-\left(b-c\right)^2\)
\(=\left(a+b-c+b-c\right)\left(a+b-c-b+c\right)\)
\(+\left(a-b+c+b-c\right)\left(a-b+c-b+c\right)\)
\(=a\left(a+2b-2c\right)+a\left(a-2b\right)\)
\(=a\left(a+2b-2c+a-2b\right)=a\left(2a-2c\right)=2a^2-2ac\)
B2:
\(\)\(x+y=3=>\left(x+y\right)^2=9=>x^2+2xy+y^2=9\)
\(=>xy=\dfrac{9-\left(x^2+y^2\right)}{2}=\dfrac{9-\left(17\right)}{2}=-4\)
\(=>x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3\left(17+4\right)=63\)
Bài 1:
a) Ta có: \(\left(x+y\right)^2-\left(x-y\right)^2\)
\(=x^2+2xy+y^2-x^2+2xy+y^2\)
=4xy
b) Ta có: \(\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y-x+y\right)^2\)
\(=\left(2y\right)^2=4y^2\)
c) Ta có: \(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x^3-1\right)\left(x^3+1\right)\)
\(=x^6-1\)
d) Ta có: \(\left(a+b-c\right)^2+\left(a+b+c\right)^2-2\left(b-c\right)^2\)
\(=\left(a+b-c\right)^2-\left(b-c\right)^2+\left(a+b+c\right)^2-\left(b-c\right)^2\)
\(=\left(a+b-c-b+c\right)\left(a+b-c+b-c\right)+\left(a+b+c-b+c\right)\left(a+b+c+b-c\right)\)
\(=a\cdot\left(a+2b-2c\right)+\left(a+2c\right)\left(a-2b\right)\)
\(=a^2+2ab-2ac+a^2-2ab+2ac-4bc\)
\(=2a^2-4bc\)
Bài 2:
Ta có: x+y=3
nên \(\left(x+y\right)^2=9\)
\(\Leftrightarrow2xy+17=9\)
\(\Leftrightarrow2xy=-8\)
hay xy=-4
Ta có: \(x^3+y^3\)
\(=\left(x+y\right)^3-3xy\left(x+y\right)\)
\(=3^3-3\cdot\left(-4\right)\cdot3\)
\(=27+36=63\)
Rút gọn :
a. ( x + 2 ) ( x2 - 2x + 4 ) - ( 1 - 3x ) ( 1 + 3x + 9x2)
b . ( x + y ) ( y2 - 2y + 4 ) + ( 5 - y ) ( 25 + 5y + y2)
a: =x^3+8-1+27x^3=28x^3+7
b: Sửa đề: (2+y)(y^2-2y+4)+(5-y)(25+5y+y^2)
=8+y^3+125-y^3
=133
Bài 1: Rút gọn biểu thức
B= (x+y)2-2(x2-y2)+(x-y)2
\(=\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2=\left(x+y-x+y\right)^2=4y^2\)
Rút gọn biểu thức x(x − y) − y(y − x) ta được ?
(A) x 2 + y 2
(B) x 2 - y 2
(C) x 2 - x y
(D) x - y 2
Hãy chọn kết quả đúng.
Ta có:
x x - y - y y - x = x 2 - x y - y 2 - x y = x 2 - x y - y 2 + x y = x 2 - y 2
Chọn (B) x 2 - y 2
Lời giải:
a. $=(x-y)(x+y)=[(-1)-(-3)][(-1)+(-3)]=2(-4)=-8$
b. $=3x^4-2xy^3+x^3y^2+3x^2y+12xy+15y-12xy-12$
$=3x^4-2xy^3+x^3y^2+3x^2y+15y-12$
=3-2.1(-2)^3+1^3.(-2)^2+3.1^2(-2)+15(-2)-12$
$=-25$
c.
$=2x^4+3x^3y-4x^3y-12xy+12xy=2x^4-x^3y$
$=x^3(2x-y)=(-1)^3[2(-1)-2]=-1.(-4)=4$
d.
$=2x^2y+4x^2-5xy^2-10x+3xy^2-3x^2y$
$=(2x^2y-3x^2y)+4x^2+(-5xy^2+3xy^2)-10x$
$=-x^2y+4x^2-2xy^2-10x$
$=-3^2.(-2)+4.3^2-2.3(-2)^2-10.3=0$