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7, 4x mũ 2 - 12x + 9 - y mũ 2 = -(y-2x+3) (y+2x-3)
8, 16x mũ 2 - 4y mũ 2 + 4y - 1 = -(2y - 4x - 1) (2y+4x-1)
9, 25 - x mũ 2 - 12x - 36 = -(x+1) (x+11)
10, x mũ 2 - 9 - 5 ( x + 3 ) = (x-8) (x+3)
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Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM
1/ \(4x^2-12xy+9y^2=\left(2x\right)^2-2.2.3xy+\left(3y\right)^2\)
\(=\left(2x-3y\right)^2\)
2/ \(x^3-y^6=x^3-\left(y^2\right)^3\)
\(=\left(x-y^2\right)\left(x^2+xy^2+y^4\right)\)
Làm tạm 2 phần đợi mik xíu
4x2 - 12xy + 9y2 = ( 2x )2 - 2.2x.3y + ( 3y )2 = ( 2x - 3y )2
x3 - y6 = x3 - ( y2 )3 = ( x - y2 )( x2 + xy2 + y4 )
x6 - 6x4 + 12x2 - 8 = ( x2 )3 - 3.(x2)2.2 + 3.x2.22 - 23 = ( x2 - 2 )3
( x2 + 4y2 - 5 )2 - 16( x2y2 + 2xy + 1 ) = ( x2 + 4y2 - 5 )2 - 42( xy + 1 )2
= ( x2 + 4y2 - 5 )2 - ( 4xy + 4 )2
= [ ( x2 + 4y2 - 5 ) - ( 4xy + 4 ) ][ ( x2 + 4y2 - 5 ) + ( 4xy + 4 ) ]
= ( x2 + 4y2 - 5 - 4xy - 4 )( x2 + 4y2 - 5 + 4xy + 4 )
= [ ( x2 - 4xy + 4y2 ) - 9 ][ ( x2 + 4xy + 4y2 ) - 1 ]
= [ ( x - 2y )2 - 32 ][ ( x + 2y )2 - 12 ]
= ( x - 2y - 3 )( x - 2y + 3 )( x + 2y - 1 )( x + 2y + 1 )
( a + b )3 - ( a3 + b3 ) = a3 + 3a2b + 3ab2 + b3 - a3 - b3
= 3a2b + 3ab2
= 3ab( a + b )
f) = x2( x - 4 ) - 9( x - 4 ) = ( x - 4 )( x - 3 )( x + 3 )
g) = 4( x - y ) + ( x - y )2 = ( x - y )( x - y + 4 )
h) = x3( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i) = ( x - y )( x + y ) - 4( x + y ) = ( x + y )( x - y - 4 )
j) = ( x - y )( x2 + xy + y2 ) - 3( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
Trả lời:
f, x3 - 4x2 - 9x + 36 = ( x3 - 4x2 ) - ( 9x - 36 ) = x2 ( x - 4 ) - 9 ( x - 4 ) = ( x - 4 )( x2 - 9 ) = ( x - 4 )( x - 3 )( x + 3 )
g, 4x - 4y + x2 - 2xy + y2 = ( 4x - 4y ) + ( x2 - 2xy + y2 ) = 4 ( x - y ) + ( x - y )2 = ( x - y ) ( 4 + x - y )
h, x4 + x3 + x2 - 1 = ( x4 + x3 ) + ( x2 - 1 ) = x3 ( x + 1 ) + ( x - 1 )( x + 1 ) = ( x + 1 )( x3 + x - 1 )
i, x2 - y2 - 4x - 4y = ( x2 - y2 ) - ( 4x + 4y ) = ( x - y )( x + y ) - 4 ( x + y ) = ( x + y )( x - y - 4 )
j, x3 - y3 - 3x + 3y = ( x3 - y3 ) - ( 3x - 3y ) = ( x - y )( x2 + xy + y2 ) - 3 ( x - y ) = ( x - y )( x2 + xy + y2 - 3 )
s) = ( x2 - 2xy + y2 ) - ( 2xy )2 = ( x - y - 2xy )( x - y + 2xy )
u) sửa +4y thành -4y
= 4( x - y ) - x2( x - y ) = ( x - y )( 2 - x )( 2 + x )
a)\(6x-9-x^2\)
\(=-\left(x^2+6x+9\right)\)
\(=-\left(x+3\right)^2\)
b)\(x^2+4y^2+4xy\)
\(=\left(x+2y\right)^2\)
c)\(x^2+8x+16\)
\(=\left(x+4\right)^2\)
d)\(9x^2-12xy+4y^2\)
\(=\left(3x-2y\right)^2\)
e)\(-25x^2y^2+10xy-1\)
\(=-\left(25x^2y^2-10xy+1\right)\)
\(=-\left(5xy-1\right)^2\)
f)\(4x^2-4x+1\)
\(=\left(2x-1\right)^2\)
j)\(x^2+6x+9\)
\(=\left(x+3\right)^2\)
h)\(9x^2-6x+1\)
\(=\left(3x-1\right)^2\)
#H
a, 6x - 9 - x2 = - x2 + 6x - 9 = - (x2 - 6x + 9) = - (x - 3)2
b, x2 + 4y2 + 4xy = x2 + 2. x . 2y + (2y)2 = (x + 2y)2
c, x2 + 8x + 16 = x2 + 2 . x . 4 + 42 = (x + 4)2
d, 9x2 - 12xy + 4y2 = (3x)2 - 2 . 3x . 2y + (2y)2 = (3x - 2y)2
e, - 25x2y2 + 10xy - 1 = - (25x2y2 - 10xy + 1) = - [(5xy)2 - 2 . 5xy + 1] = - (5xy - 1)2
f, 4x2 - 4x + 1 = (2x)2 - 2 . 2x + 1 = (2x - 1)2
j, x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
h, 9x2 - 6x + 1 = (3x)2 - 2 . 3x + 1 = (3x - 1)2
Trả lời:
7, 49y2 - x2 + 6x - 9
= 49y2 - ( x2 - 6x + 9 )
= ( 7y )2 - ( x - 3 )2
= ( 7y - x + 3 ) ( 7y - x - 3 )
8, sửa đề: 25x2 - 4y2 - 4y - 1
= 25x2 - ( 4y2 + 4y + 1 )
= ( 5x )2 - ( 2y + 1 )
= ( 5x - 2y - 1 ) ( 5x + 2y + 1 )
9, 4x2 - y2 + 8y - 16
= 4x2 - ( y2 - 8y + 16 )
= ( 2x )2 - ( y - 4 )2
= ( 2x - y + 4 ) ( 2x + y - 4 )
a, \(49y^2-x^2+6x-9=49y^2-\left(x-3\right)^2=\left(7y-x+3\right)\left(7y+x-3\right)\)
b, đề sai rồi bạn
c, \(4x^2-y^2+8y-16=4x^2-\left(y-4\right)^2=\left(2x-y+4\right)\left(2x+y-4\right)\)
\(1,\)
\(\left(x^2-9y^2\right)\left(4x+12y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)-4\left(x+3y\right)\)
\(=\left(x+3y\right)\left(x-3y-4\right)\)
\(3,\)
\(-x^2+2xy-y^2+25\)
\(=-\left(x^2-2xy+y^2\right)+25\)
\(=25-\left(x-y\right)^2\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(5-x+y\right)\left(5+x-y\right)\)
6, \(x^2-1+2xy+y^2=\left(x+y\right)^2-1=\left(x+y-1\right)\left(x+y+1\right)\)
7, \(4x^2-12x+9-y^2=\left(2x-3\right)^2-y^2=\left(2x-3-y\right)\left(2x-3+y\right)\)
8, \(16x^2-4y^2+4y-1=16x^2-\left(2y-1\right)^2=\left(4x-2y+1\right)\left(4x+2y-1\right)\)
9, \(25-x^2-12x-36=25-\left(x+6\right)^2=\left(5-x-6\right)\left(5+x+5\right)=-\left(x+1\right)\left(x+10\right)\)
10, \(x^2-9-5\left(x+3\right)=\left(x-3\right)\left(x+3\right)-5\left(x+3\right)=\left(x+3\right)\left(x-8\right)\)