Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a, 3x - 3y = 3( x- y )
b, x2 - x =x(x - 1)
c, 3(x - y) - 5x(y - x)
= 3(x - y) + 5x(x - y)
= ( x - y)(3 + 5x)
d, x(y - 1) - y(y - 1)
= (x - y)(y - 1)
e, 10x(x - y)-8y( y - x)
= 10x(x - y) + 8y(x - y)
= (10y + 8x)(x - y)
f, 2x2 +5x3 +xy
= x(2x + 5x2 + y)
g, 14x2y - 21xy2 +28x2y2
= 7xy(2x - 3y + 4xy)
h, x2 - 3x + 2
= x2 - x - 2x + 2
= x(x - 1)- 2(x - 1)
= (x - 2)(x - 1)
i, x2 - x - 6
x2 + 2x - 3x - 6
x(x + 2) - 3(x + 2)
(x + 2)(x - 3)
k, x2 + 5x+6
= x2 - x + 6x + 6
=x(x - 1) + 6(x + 1)
= x(x - 1) - 6(x - 1)
= (x - 6)(x - 1)
l,x2 - 4x + 3
= x2 - x - 3x + 3
= x(x - 1) - 3(x - 1)
= (x - 3)(x - 1)
m, x2 + 5x +4
= x2 + x + 4x + 4
= x(x + 1) + 4(x + 1)
= (x + 4)(x + 1)
a) \(\left(3x-5\right)\left(2x+3\right)-\left(2x-3\right)\left(3x+7\right)-2x\left(x-4\right)\)
\(=\left(6x^2-x-15\right)-\left(6x^2+5x-21\right)-\left(2x^2-8x\right)\)
\(=6x^2-x-15-6x^2-5x+21-2x^2+8x\)
\(=-2x^2+2x+6\)
\(=-2\left(x^2-x-3\right)\)
b) \(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^2-4\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^4-16\right)\)
\(=\left(x^4+4x^2+4\right)-\left(x^4-16\right)\)
\(=x^4+4x^2+4-x^4+16\)
\(=4x^2+20\)
\(=4\left(x^2+5\right)\)
c) \(\left(2x-y\right)^2-2\left(x+3y\right)^2-\left(1+3x\right)\left(3x-1\right)\)
\(=\left(4x^2-4xy+y^2\right)-2\left(x^2+6xy+9y^2\right)-\left(9x^2-1\right)\)
\(=4x^2-4xy+y^2-2x^2-16xy-18y^2-9x^2+1\)
\(=-7x^2-20xy-17y^2+1\)
d) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^6-3x^4+3x^2-1\right)-\left(x^6-1\right)\)
\(=x^6-3x^4+3x^2-1-x^6+1\)
\(=-3x^4+3x^2\)
\(=-3x^2\left(x^2-1\right)\)
\(=-3x^2\left(x-1\right)\left(x+1\right)\)
e) \(\left(2x-1\right)^2-2\left(4x^2-1\right)+\left(2x+1\right)^2\)
\(=\left(2x-1\right)^2-2\left(2x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)
\(=\left[\left(2x-1\right)-\left(2x+1\right)\right]^2\)
\(=\left(2x-1-2x-1\right)^2\)
\(=\left(-2\right)^2=4\)
g) \(\left(x-y+z\right)^2+\left(y-z\right)^2-2\left(x-y+z\right)\left(z-y\right)\)
\(=\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)
\(=\left(x-y+z+y+z\right)^2\)
\(=\left(x+2z\right)^2\)
h) \(\left(2x+3\right)^2+\left(2x+5\right)^2-\left(4x+6\right)\left(2x+5\right)\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\)
\(=\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\)
\(=\left(2x+3-2x-5\right)^2\)
\(=\left(-2\right)^2=4\)
i) \(5x^2-\dfrac{10x^3+15x^2-5x}{-5x}-3\left(x+1\right)\)
\(=5x^2-\dfrac{-5x\left(-2x^2-3x+1\right)}{-5x}-3\left(x+1\right)\)
\(=5x^2-\left(-2x^2-3x+1\right)-3\left(x+1\right)\)
\(=5x^2+2x^2+3x-1-3x-3\)
\(=7x^2-4\)
a) Bình phương \(x+\frac{1}{x}=3\)
Kết quả: 7
b) Lập phương \(x+\frac{1}{x}=3\)
Kết quả: 18
c) Bình phương \(x^2+\frac{1}{x^2}\)
Kết quả: 47
a) \(7x^3y-14x^2y+7xy\)
\(=7xy\left(x^2-2x+1\right)\)
\(=7xy\left(x-1\right)^2\)
b) \(x^2-9+\left(x-3\right)^2\)
\(=\left(x-3\right)\left(x+3\right)+\left(x-3\right)^2\)
\(=\left(x-3\right)\left(x+3+x-3\right)\)
\(=2x\left(x-3\right)\)
c) \(x^3-4x^2-12x+27\)
\(=x^3+3x^2-7x^2-21x+9x+27\)
\(=x^2\left(x+3\right)-7x\left(x+3\right)+9\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
d) \(x^3+y^3+z^3-3xyz\)
\(=\left(x+y\right)^3-3xy\left(x+y\right)+z^3-3xyz\)
\(=\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2\right)-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xz-yz+2xy-3xy\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xz-yz-xy\right)\)
a) 3( x - y ) - 5x( y - x )
= 3( x - y ) - 5x[ -( x - y ) ]
= 3( x - y ) + 5x( x - y )
= ( 3 + 5x )( x - y )
b) x3 + 2x2y + xy2 - 9x
= x( x2 + 2xy + y2 - 9 )
= x[ ( x + y )2 - 32 ]
= x( x + y - 3 )( x + y + 3 )
c) 14x2y - 21xy2 + 28x2y2
= 7xy( 2x - 3y + 4xy )
Bài giải
\(a,\text{ }3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
\(b,\text{ }x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y+3\right)\left(x+y-3\right)\)
\(c,\text{ }14x^2y-21xy^2+28x^2y\)
\(=7xy\left(2x-3y+4x\right)\)
\(=7xy\left(6x-3y\right)\)
\(2x^6+3x^3y^3+y^6+y^3=2x^6+2x^3y^3+x^3y^3+y^6+y^3=2x^3\left(x^3+y^3\right)+y^3\left(x^3+y^3\right)+y^3=2x^3\left(x^3+y^3\right)+y^3\left(x^3+y^3+1\right)=2x^3×1+y^3×2=2\left(x^3+y^3\right)=2\)
A=\(x^3-2x^2+x\)
=x.(x2-2x+1)
=x(x-1)2
B=\(2x^2+4x+2-2y^2\)
=\(2\left(x^2+2x+1-y^2\right)\)
=\(2.\left[\left(x+1\right)^1-y^2\right]\)
=\(2\left(x+1-y\right)\left(x+1+y\right)\)
C=\(2xy-x^2-y^2+16\)
=\(-\left(-2xy+x^2+y^2-16\right)\)
=\(-\left[\left(x-y\right)^2-4^2\right]\)
=-(x-y-4)(x-y+4)
D=\(x^3+2x^2y+xy^2-9x\)
=\(x\left(x^2+2xy-y^2-9\right)\)
=\(x.\left[\left(x-y\right)^2-3^2\right]\)
=x.(x-y-3)(x-y+3)
E=\(2x-2y-x^2+2xy-y^2\)
\(=\left(2x-2y\right)-\left(x^2-2xy+y^2\right)\)
=\(2\left(x-y\right)-\left(x-y\right)\left(x-y\right)\)
=(x-y)(2x-2y-x+y)
=(x-y)(x+y)
Vy Lê: bạn ơi hướng làm của bài là khai triển biểu thức đơn giản và phát hiện 1 số biểu thức có liên quan đến hằng đẳng thức thôi nên mình nghĩ mình làm như vậy cũng có ngắn lắm đâu nhỉ? Ví dụ như câu c chả hạn. $(2x+3)(4x^2-6x+9)=(2x)^3+3^3$ là hằng đẳng thức đáng nhớ rồi nên mình áp dụng luôn. $2(4x^3-3)=8x^3-6$ theo khai triển thông thường.
Lời giải:
a)
$(-x-3)^3+(x+9)(x^2+27)$
$=(x+9)(x^2+27)-(x+3)^3$
$=x^3+27x+9x^2+243-(x^3+9x^2+27x+27)$
$=216$
b)
$(x+2)^3-x(x^2+6x-5)-8$
$=x^3+6x^2+12x+8-x^3-6x^2+5x-8$
$=17x$
c)
$(2x+3)(4x^2-6x+9)-2(4x^3-3)$
$=(2x)^3+3^3-2(4x^3-3)=8x^3+27-8x^3+6=33$
\(\text{∘}\) \(\text{Ans}\)
\(\downarrow\)
\(14x^2y^3-7xy^2\cdot\left(2x-3y\right)\)
`=`\(14x^2y^3-\left[7xy^2\cdot2x+7xy^2\cdot\left(-3y\right)\right]\)
`=`\(14x^2y^3-\left(14x^2y^2-21xy^3\right)\)
`=`\(14x^2y^3-14x^2y^2+21xy^3\)
\(\text{∘}\) \(\text{Kaizuu lv uuu.}\)