Triển khai giúp mình
a) ( 5x - x^2 ) . ( 5 + x^2 )
b) ( 2x - y ) . ( 4x^2 + 2xy + y^2)
c) ( x + 3) . ( x^2 - 3x + 9)
d) -x3 + 3x^2 - 3x + 1
e) x^2 - 2x + 9
g) ( x + 1) . ( x-1)
h) ( x -2y) . ( x + 2y)
i) 25a^2 + 4b^2 - 20ab
Triển khai giúp mình ạ
a) ( 2 + xy )^2
b) ( 5 - x^2 ) . ( 5 + x^2 )
c ) ( 2x - y ) . ( 4x^2 + 2xy + y^2 )
d) ( 5 - 3x )^2
e) ( 5x - 1 ) ^3
f) ( x + 3 ) . ( x^2 - 3x + 9)
g) -x^3 + 3x^2 - 3x + 1
h)( 2x^2 + 3y)^2
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) 3x 2 (2x 3 – x + 5)
b) (4xy + 3y – 5x)x 2 y
c) (3x 2 y – 6xy + 9x)(- 3
4
xy)
d) - 3
1
xz(- 9xy + 15yz) + 3x 2 (2yz 2 – yz)
e) (x 3 + 5x 2 – 2x + 1)(x – 7)
f) (2x 2 – 3xy + y 2 )(x + y)
g) (x – 2)(x 2 – 5x + 1) – x(x 2 + 11)
h) [(x 2 – 2xy + 2y 2 )(x + 2y) - (x 2 + 4y 2 )(x – y)] 2xy
Mọi người giúp em với ạ
Đề bài là gì sao không ghi rõ??
a. 3x^2-3y^2-x-y
b. 2x^2+4xy-16+2y^2
c. -x^2-x+2
d. 3x^2-7x+4
e.-2x^2+3x-1
f. x^2+2xy+y^2-2x-2y
g.x^3-2x^2+1
h.4x^2-3x-1
k. 2x^2+5x+3
l. x^2-2x-y^2+1
a) \(3x^2-3y^2-x-y\)
\(\Leftrightarrow3\left(x^2-y^2\right)-x-y\)
\(\Leftrightarrow3\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(\Leftrightarrow3\left(x-y\right)\)
d) \(3x^2-7x+4\)
\(\Leftrightarrow3x^2-7x+7-3\)
\(\Leftrightarrow\left(3x^2-3\right)-\left(7x-7\right)\)
\(\Leftrightarrow3\left(x^2-1\right)-7\left(x-1\right)\)
\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-7\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(3\left(x+1\right)-7\right)\)
\(\Leftrightarrow\left(x+1\right)\left(3x-6\right)\)
e) \(-2x^2+3x-1\)
\(\Leftrightarrow\left(-2x^2-1^2\right)+3x\)
\(\Leftrightarrow\left(-2x-1\right)\left(-2x+1\right)+3x\)
f) \(x^2+2xy+y^2-2x-2y\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
k) \(2x^2+5x+3\)
\(\Leftrightarrow2x^2+2x+3x+3\)
\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)\)
\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\)
l) \(x^2-2x-y^2+1\)
\(\Leftrightarrow\left(x^2-2x+1\right)-y^2\)
\(\Leftrightarrow\left(x-1\right)^2-y^2\)
\(\Leftrightarrow\left(x-1-y\right)\left(x-1+y\right)\)
a) \(3x^2-3y^2-x-y\)
\(\Leftrightarrow3\left(x^2-y^2\right)-x-y\)
\(\Leftrightarrow3\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(\Leftrightarrow3\left(x-y\right)\)
d) \(3x^2-7x+4\)
\(\Leftrightarrow3x^2-7x+7-3\)
\(\Leftrightarrow\left(3x^2-3\right)-\left(7x-7\right)\)
\(\Leftrightarrow3\left(x^2-1\right)-7\left(x-1\right)\)
\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-7\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(3\left(x+1\right)-7\right)\)
\(\Leftrightarrow\left(x+1\right)\left(3x-6\right)\)
e) \(-2x^2+3x-1\)
\(\Leftrightarrow\left(-2x^2-1^2\right)+3x\)
\(\Leftrightarrow\left(-2x-1\right)\left(-2x+1\right)+3x\)
f) \(x^2+2xy+y^2-2x-2y\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
k) \(2x^2+5x+3\)
\(\Leftrightarrow2x^2+2x+3x+3\)
\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)\)
\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\)
l) \(x^2-2x-y^2+1\)
\(\Leftrightarrow\left(x^2-2x+1\right)-y^2\)
\(\Leftrightarrow\left(x-1\right)^2-y^2\)
\(\Leftrightarrow\left(x-1-y\right)\left(x-1+y\right)\)
B1: quy đồng mẫu số các phân thức:
a. 5/ 6x^2y ; 7/ 12xy^2 ; 11/ 18xy
b. 4x+2/ 15x^3y ; 5y - 3/ 9x^2y ; x+1/5xy^3
c. 3/2x ; 3x-3/2x-1 ; 3x-2/2x- 4x^2
d. x^3 + 2x / x^3+1 ; 2x/ x^2 - x +1 ; 1/ x+1
e. y/ 2x^2 - xy ; 4x/ y^2 - 2xy
f. 1/x+2 ; 3/ x^2 - 4 ; x-14/ ( x^2 + 4x + 4 ) (x-2)
g. 1/x+2 ; 1/ (x+2)(4x+7) ;
h. 1/x+3 ; 1/ (x+3)(x+2) ; 1/ (x+2)(4x+7)
B2: dùng quy tắc đổi dấu để tìm mẫu thức chung :
a.4/ x+2 ; 2/x-2 ; 5x-6/4-x^2
b. 1-3x/2x ; 3x-2/2x-1 ; 3x-2/2x-4x^2
c. 1/ x^2 + 6x + 9 ; 1/ 6x-x^2-9 ; x/ x^2 -9
d. x^2 + 2/ x^3 - 1 ; 2/ x^2 + x +1 ; 1/ 1-x
e. x/ - 2y ; x/ x+2y ; 4xy/ 4y^2 - x^2
Ai làm xong trước mình tick nha!
Bài 1: Thực hiện phép tính
a) 3x(2x2 - 5x + 9)
b) 5x(x2-xy+1)
c) -2/3x2y(3xy-x2+y)
2) Thực hiện phép tính
a) (5x-2y) (x2-xy+1)
b) (x+3y)(x2-2xy+y)
c) (3x-5y) (4x+ 7y)
Bài 3: Rút gọn các biểu thức sau(bằng cách khai triển hằng đẳng thức):
a) (x+y)2+(x-y)2
b) (x+2)(x-2)-(x-3)(x+1)
c) (x-2)(x+2)-(x-2)2
d) (2x+y)(4x2-2xy+y2)-(2x-y)(4x2+2xy+y2)
Bài 1: Thực hiện phép tính
a) 3x(2x2 - 5x + 9) = \(6x^3-15x^2+27x\)
b) 5x(x2-xy+1) = \(5x^3-5xy+5x\)
c) -2/3x2y(3xy-x2+y) = \(-2x^3y^2+\dfrac{2}{3}x^4y-\dfrac{2}{3}x^2y^2\)
2) Thực hiện phép tính
a) (5x-2y) (x2-xy+1) = \(5x^3+5x-7y-2x^3y+2xy^2\)
b) (x+3y)(x2-2xy+y) = \(x^3-x^2y+xy+6xy^2+y^2\)
c) (3x-5y) (4x+ 7y) = \(12x^2-xy-35y^2\)
Bài 3: Rút gọn các biểu thức sau(bằng cách khai triển hằng đẳng thức):
a) (x+y)2+(x-y)2
= \(x^2+2xy+y^2+x^2-2xy+y^2\)
= \(\left(x^2+x^2\right)+\left(2xy-2xy\right)+\left(y^2+y^2\right)\)
= \(2x^2+2y^2=2\left(x^2+y^2\right)\)
b) (x+2)(x-2)-(x-3)(x+1)
= \(x^2-4\) - \(\left(x^2-2x-3\right)\)= \(x^2-4-x^2+2x+3\)
= \(\left(x^2-x^2\right)+2x+\left(-4+3\right)\)=\(2x-1\)
c) (x-2)(x+2)-(x-2)2
=>\(x^2-4-\left(x^2-2.x.2+2^2\right)=x^2-4-x^2-4x+4=\left(x^2-x^2\right)+\left(-4+4\right)-4x=-4x\)
d) (2x+y)(4x2-2xy+y2)-(2x-y)(4x2+2xy+y2)
= \(8x^3+y^3-\left(8x^3-y^3\right)\)
= \(8x^3+y^3-8x^3+y^3\)
= \(\left(8x^3-8x^3\right)+\left(y^3+y^3\right)\)= \(2y^3\)
phân tích đa thức thành nhân tử
a) 2x^2 - 2y^2
b) x^2 -4x + 4
c) x^2 + 2x + 1 - y^2
d) x^2 - 4x
e) x^2 + 10x + 25
g) x^2 -2xy + y ^2 - 9
h) 2x^2 - 2
i) 5x^2 - 5xy + 9x - 9y
k) y^2 - 4y + 4 - x^2
l)x^2 - 16
m) 3x^2 -3xy +2x - 2y
o) 3x^4 - 6x ^3 + 3x^2
a) \(2x^2-2y^2\)
\(=2\left(x^2-y^2\right)\)
\(=2\left(x-y\right)\left(x+y\right)\)
b) \(x^2-4x+4\)
\(=x^2-2\cdot x\cdot2+2^2\)
\(=\left(x-2\right)^2\)
c) \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x-y+1\right)\left(x+y+1\right)\)
d) \(x^2-4x\)
\(=x\left(x-4\right)\)
e) \(x^2+10x+25\)
\(=x^2+2\cdot x\cdot5+5^2\)
\(=\left(x+5\right)^2\)
g) \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-3^2\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
h) \(2x^2-2\)
\(=2\left(x^2-1\right)\)
\(=2\left(x-1\right)\left(x+1\right)\)
i) \(5x^2-5xy+9x-9y\)
\(=5x\left(x-y\right)+9\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+9\right)\)
k) \(y^2-4y+4-x^2\)
\(=\left(y-2\right)^2-x^2\)
\(=\left(y-x-2\right)\left(y+x-2\right)\)
l) \(x^2-16\)
\(=x^2-4^2\)
\(=\left(x-4\right)\left(x+4\right)\)
m) \(3x^2-3xy+2x-2y\)
\(=3x\left(x-y\right)+2\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+2\right)\)
o) \(3x^4-6x^3+3x^2\)
\(=3x^2\left(x^2-2x+1\right)\)
\(=3x^2\left(x-1\right)^2\)
a) 2x2 - 2y2
= (2x - 2y)(2x + 2y)
= 4(x - y)(x + y)
b) x2 - 4x + 4
= (x - 2)2
c) x2 + 2x + 1 - y2
= (x + 1)2 - y2
= (x + 1 - y)(x + 1 + y)
d) x2 - 4x
= x(x - 4)
e) x2 +10x + 25
= (x + 5)2
g) x2 - 2xy + y2 - 9
= (x - y)2 - 32
= (x - y - 3)(x - y + 3)
h) 2x2 - 2
= 2(x2 - 1)
= 2(x - 1)(x + 1)
i) 5x2 - 5xy + 9x - 9y
= 5x(x - y) + 9(x- y)
= (5x + 9)(x - y)
k) y2 - 4y + 4 - x2
= (y - 2)2 - x2
= (y - 2 - x)(y - 2 + x)
l) x2 - 16
= x2 - 42
= (x - 4)(x + 4)
m) 3x2 - 3xy + 2x -2y
= 3x(x - y) +2(x-y)
= (3x + 2)(x - y)
o) 3x4 - 6x3 + 3x2
= 3x4 - 3x3 - 3x3 + 3x2
= 3x3(x - 1) - 3x2(x - 1)
= (3x3 - 3x2)(x - 1)
= 3x2(x - 1)(x - 1)
= 3x2.(x - 1)2
Bài 1: Rút gọn các biểu thức:
a. (2x - 1)2 - 2(2x - 3)2 + 4
b. (3x + 2)2 + 2(2 + 3x)(1 - 2y) + (2y - 1)2
c. (x2 + 2xy)2 + 2(x2 + 2xy)y2 + y4
d. (x - 1)3 + 3x(x - 1)2 + 3x2(x -1) + x3
e. (2x + 3y)(4x2 - 6xy + 9y2)
f. (x - y)(x2 + xy + y2) - (x + y)(x2 - xy + y2)
g. (x2 - 2y)(x4 + 2x2y + 4y2) - x3(x – y)(x2 + xy + y2) + 8y3
a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
3A. Tính giá trị biểu thức: a) A = (x²-3x² + 3x)² -2(x²-3x² + 3x)+1 tại x= 11; b) B=(x-2y)(x² + 2xy + 4y²)-6xy(x-2y) tai x=3;y=; 5A. Phân tích đa thức thành nhân tử a) x² +1-2x²; c) y²-4x² + 4x-1; b)x²-y²-5y+5x; d) x (2+x)²-(x+2)+1-x² 6A. Phân tích đa thức thành nhân tử: (a) x² −8x+7; b) 2x² -5x+2; c) x²-5x² +8x-4; d) x² +64.