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a ) \(x^3+3x^2-3x+1\)
\(=x^3-3x+3x^2-1\)
\(=\left(x-1\right)^3\)
Bài 1:
a: \(3x\left(x-a\right)+4a\left(a-x\right)\)
=3x(x-a)-4a(x-a)
=(x-a)(3x-4a)
b: \(x^2\left(y^2+z\right)+y^3+yz\)
\(=x^2\left(y^2+z\right)+y\left(y^2+z\right)\)
\(=\left(x^2+y\right)\left(y^2+z\right)\)
c: \(3x^2\left(x+1\right)-5x\left(x+1\right)^2+4\left(x+1\right)\)
\(=\left(x+1\right)\left[3x^2-5x\left(x+1\right)+4\right]\)
\(=\left(x+1\right)\left(3x^2-5x^2-5x+4\right)\)
\(=\left(x+1\right)\left(-2x^2-5x+4\right)\)
Bài 4.
a) 3xy2 - 45x2y = 3xy( y - 15x )
b) 25y2 - 4x2 + 4x - 1
= 25y2 - ( 4x2 - 4x + 1 )
= ( 5y )2 - ( 2x - 1 )2
= ( 5y - 2x + 1 )( 5y + 2x - 1 )
c) x2 - 5x + xy - 5y
= x( x - 5 ) + y( x - 5 )
= ( x - 5 )( x + y )
d) x2 - 8x - 33
= x2 + 3x - 11x - 33
= x( x + 3 ) - 11( x + 3 )
= ( x + 3 )( x - 11 )
Bài 5.
a) A = ( x - 2 )3 - x2( x - 4 ) + 8
= x3 - 6x2 + 12x - 8 - x3 + 4x2 + 8
= -2x2 + 12x
B = ( x2 - 6x + 9 ) : ( x - 3 ) - x( x + 7 ) - 9
= ( x - 3 )2 : ( x - 3 ) - x2 - 7x - 9
= x - 3 - x2 - 7x - 9
= -x2 - 6x - 12
b) Với x = -1 thì A = -2.(-1)2 + 12.(-1) = -2 - 12 = -14
a) x3 + 2x - 3
=x3+x2+3x-x2+x+3
=x(x2+x+3)-1(x2+x+3)
=(x-1)(x2+x+3)
b) x3 - x2 + x + 3
=x3-2x2+3x+x2-2x+3
=x(x2-2x+3)+1(x2-2x+3)
=(x+1)(x2-2x+3)
c) 3x3 - 4x2 + 13x - 4
=3x3-3x2+12-x2-x+4
=3x(x2-x+4)-1(x2-x+4)
=(3x-1)(x2-x+4)
d) 6x3 + x2 + x + 1
=6x3-2x2+2x+3x2-x+1
=2x(3x2-x+1)+1(3x2-x+1)
=(2x+1)(3x2-x+1)
e)bạn phân tích tương tự nhé mk cho đáp án để bạn đổi chiếu nè
=(2x+1)(2x2+2x+1)
a) 1/2(x3+8)=1/2(x+2)(x2-2x+4)
b) x4(x-y)+2x3(x-y)=x3(x+2)(x-y)
c) x2-(y2-6y+9)=x2-(y-3)2=(x-y+3)(x+y-3)
d) xy(x3+y3)=xy(x+y)(x2-xy+y2)
e)3x2(x2-25y2)=3x2(x-5y)(x+5y)
f) 4x4+4x2y2+y4-4x2y2= (2x2+y2)2-(2xy)2=(2x2-2xy+y2)(2x2+2xy+y2)
a) \(\frac{1}{2}x^3+4=\frac{1}{2}\left(x^3+8\right)=\frac{1}{2}\left(x+2\right)\left(x^2-2x+4\right)\)
b) \(x^5-x^4y+2x^4-2x^3y=x^3\left(x^2-xy+2x-2y\right)=x^3\left[x\left(x-y\right)+2\left(x-y\right)\right]=x^2\left(x-y\right)\left(x+2\right)\)
c) \(x^2-y^2+6y-9=x^2-\left(y-3\right)^2=\left(x+y-3\right)\left(x-y+3\right)\)
d) \(x^4y+xy^4=xy\left(x^3+y^3\right)=xy\left(x+y\right)\left(x^2-xy+y^2\right)\)
e) \(3x^4-75x^2y^2=3x^2\left(x^2-25y^2\right)=3x^2\left(x+5y\right)\left(x-5y\right)\).
f) \(4x^4+y^4=\left(2x^2+y^2\right)^2-\left(2xy\right)^2=\left(2x^2+y^2+2xy\right)\left(2x^2-y^2-2xy\right)\)
chuyển về dạng nguyên thể rồi tính thể chất khối lượng sau đó quay về đang tìm mũ của nhiều số làm ra rồi thì dễ lắm bạn ạ k minh nha
a)\(\left(x^2-2\right)\left(x^2+2x+2\right)\)
b)\(\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\)
c)\(-2\left(x-4\right)\left(2x+1\right)\)
d)\(\left(x-5\right)\left(4x+1\right)\)
e)\(3\left(x-2\right)\left(3x-2\right)\)
g)\(2\left(a-b\right)^2\)
h)\(\left(xy-3\right)\left(5y^2-2z\right)\)
i)\(\left(4x+1\right)\left(2x-y\right)\)
l)\(abc^2\left(b-a\right)\left(b+c\right)\)
m)\(\left(x-y\right)\left(y-z\right)\left(x-z\right)\)
\(x^2-3xy-40y^2\)
\(=x^2+5xy-8xy-40y^2\)
\(=x\left(x+5y\right)-8y\left(x+5y\right)\)
\(=\left(x+5y\right)\left(x-8y\right)\)