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Câu 1 : x2-y2+2yz-z2=-(y2-2yz+z2-x2) Câu 2: x2-2xy+y2-xz+yz=(x2-2xy+y2)-xz+yz
=-(y-z)2 -x2 =(x-y)2-z(x-y)
=-(y-z-x)(y-z+x) =(x-y)(x-y-z)
\(a,x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
\(b,25-4x^2-4xy-y^2\)
\(=25-\left(4x^2+4xy+y^2\right)\)
\(=5^2-\left(2x+y\right)^2\)
\(=\left(5-2x+y\right)\left(5+2x+y\right)\)
\(c,x^3-x+y^3-y\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+1\right)\)
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 )
1 x mũ 2 + 4xy + 4y mũ 2 = x^2 + 4xy + 4y^2 =(2y+x)^2
2, 4x mũ 2 - 36y mũ 2 =4x^2 -36y^2 = -4 (3y-x) (3y+x)
\(1,x^2-y^2+4x-4y\)
\(\left(x-y\right)\left(x+y\right)+4\left(x-y\right)\)
\(\left(x-y\right)\left(x+y+4\right)\)
\(x^2+2x-4y^2-4y\)
\(\left(x-2y\right)\left(x+2y\right)+2\left(x-2y\right)\)
\(\left(x-2y\right)\left(x+2y+2\right)\)
\(3,3x^2-4y+4x-3y^2\)
\(3\left(x^2-y^2\right)-4\left(x-y\right)\)
\(3\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\)
\(\left(x-y\right)\left(3x+3y-4\right)\)
\(x^4-6x^3+54x-81\)
\(x^4+3x^3-9x^3+27x^2-27x^2+81x-27x-81\)
\(\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27x+81\right)\)
\(x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)
\(\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)
\(\left(x+3\right)\left(x-3\right)^3\)
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)
bạn k cho mình nha
chúc bạn học tốt :))))
bạn kham khảo link, mình đã làm rồi nhé
Câu hỏi của Phạm Đỗ Bảo Ngọc - Toán lớp 8 - Học trực tuyến OLM
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 )
1) \(x^2-4xy+4y^2+xz-2yz\)
\(=\left(x^2-4xy+4y^2\right)+\left(xz-2yz\right)\)
\(=\left(x-2y\right)^2+z\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-2y+z\right)\)
2) \(\left(x-y\right)^3+\left(x+y\right)^3\)
\(=\left[\left(x-y\right)+\left(x+y\right)\right]\left[\left(x-y\right)^2-\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2\right]\)
\(=\left(x-y+x+y\right)\left(x^2-2xy+y^2-x^2+y^2+x^2+2xy+y^2\right)\)
\(=2x\left(x^2+3y^2\right)\)
mik cảm ơn