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-3x4y -12x2y -12x2
= -3x2(x2y+4y+4)
4x5y2+16x4y2+16x3y2
= 4x3y2(x2+4x+4)
= 4x3y2(x+2)2
5x4y2+20x3y2+20x2y2
= 5x2y2(x2+4x+4)
= 5x2y2 (x+2)2
7x2-14x+7
= 7(x2-2x+1)
= 7(x-1)2
1, -3x4y + 6x3y - 3x2y
= -3x2y (x2 - 2x + 1)
= -3x2y(x - 1)2
2, 12x2 - 12xy + 3y2
= 3(4x2 - 4xy + y2)
= 3(2x - y)2
3, 20x4y2 - 20x3y3 + 5x2y4
= 5x2y2(4x2 - 4xy + y2)
= 5x2y2(2x - y)2
4, 16x5y2 - 16x4y3 + 4x3y4
= 4x3y2(4x2 - 4xy + y2)
= 4x3y2(2x - y)2
5, -12x4y + 12x3y2 - 3x2y3
= -3x2y(4x2 - 4xy + y2)
= -3x2y(2x - y)2
6, (a2 + 4)2 - 16a2
= (a2 + 4 - 4a)(a2 + 4 - 4a)
7, (a2 + 9)2 - 36a2
= (a2 + 32)2 - (6a)2
= (a2 + 32 - 6a)(a2 + 32 + 6a)
= (a2 - 6a + 9)(a2 + 6a + 9)
8, (a2 + 4b2)2 - 16a2b2
= (a2 + 4b2 - 4ab)(a2 + 4b2 + 4ab)
= (a2 - 4ab + 4b2)(a2 + 4ab + 4b2)
= (a - 2b)2(a + 2b)2
= (a2 - 4b2)4
Câu này có sai thì bạn thông cảm nhá!!!
9, 36a2 - (a2 + 9)2
= (6a)2 - (a2 + 9)2
=- (a2 - 6a + 9)(a2 + 6a + 9)
= -(a - 3)2(a + 3)2
= -(a2 - 9)4
Câu 10 giống câu 8 bạn nhé
1) 2x3 + 4x2 y + 2xy2
= 2x(x2 + 2xy +y2)
= 2x (x+y)2
2) -3x2 - 12x - 12
= -3(x2 + 4x +4)
=-3(x+2)2
3) 4x5 y2 + 16x4 y2 + 16x3 y2
= 4x3y2(x2 + 4x + 4)
=4x3y2 (x+2)2
4) 2x3 - 4x2 + 2x
= 2x(x2 - 2x + 1)
=2x(x-1)2
5) 5x4 y2 - 10x3 y2 + 5x2 y2
= 5x2y2(x2- 2x + 1)
=5x2y2 (x-1)2
Mong giúp đc bn.
3) =2(x2+2xy+y2)
=2(x+y)2
6)= -3(x2+4x+4)
= -3(x2+2.x.2+22)
= -3(x+2)2
9) = 4x3y2(x2+4x+4)
=4x3y2(x+2)2
12)=2x(x2-2x+1)
=2x(x-1)2
15)= 5x2y2(x2-2x+1)
=5x2y2(x-1)2
\(\text{a) }x^3y^3+x^2y^2+4\)
\(=x^3y^3+2x^2y^2-x^2y^2+4\)
\(=\left(x^3y^3+2x^2y^2\right)-\left(x^2y^2-4\right)\)
\(=x^2y^2\left(xy+2\right)-\left(xy+2\right)\left(xy-2\right)\)
\(=\left(xy+2\right)\left(x^2y^2-xy+2\right)\)
\( {c)}\)\(x^4+x^3+6x^2+5x+5\)
\(=\left(x^4+x^3+x^2\right)+\left(5x^2+5x+5\right)\)
\(=x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2+5\right)\)
\({d)}\)\(x^4-2x^3-12x^2+12x+36\)
\(=\left(x^4-2x^3-6x^2\right)-\left(6x^2-12x-36\right)\)
\(=x^2\left(x^2-2x-6\right)-6\left(x^2-2x-6\right)\)
\(=\left(x^2-2x-6\right)\left(x^2-6\right)\)
Câu b sai đề thì phải ah
1) \(12x^2-12xy+3y^2\)
\(=3\left(4x^2-4xy+y^2\right)\)
\(=3\left(2x-y\right)^2\)
5) \(4a^2-x^2-2x-1\)
\(=\left(2a\right)^2-\left(x^2+2x+1\right)\)
\(=\left(2a\right)^2-\left(x+1\right)^2\)
\(=\left(2a-x-1\right)\left(2a+x+1\right)\)
b) x3y3 + x2y2+ 4 = x3y3- 4xy + (xy)2- 2xy.2 + 22 = xy [ (xy)^2 - 2^2 ] + ( xy - 2)^2
= xy(xy-2)(xy+2)+ (xy-2)^2
= (xy-2) [ xy(xy+2) + ( xy-2) ]
= (xy-2) [ (xy)2 + 2xy + xy - 3 ]
= ( xy - 3) [ (xy)2 + 3xy - 3]
3) (chưa bik làm)
4) x4 +x3 + 6x2 +5x +5
= x4 +x3 + x2 + 5x2 + 5x +5
= x2( x2+x+ 1 ) + 5( x2+x+ 1 )
= ( x2+ 5 ) ( x2+x+ 1 )
5) x4 - 2x3 - 12x2 +12x + 36
= x4 - 2x3 - 6x2 - 6x2 + 12x + 36=
x2 ( x2 - 2x - 6) - 6 ( x2 - 2x - 6)
= (x^2 - 6) ( x2 - 2x - 6) 6) x8y8 + x4y4 + 1 = \(\left[\left(xy\right)^4\right]^2+2x^4y^4+1-x^4y^4\)=\(\left[\left(xy\right)^4+1\right]^2-\left[\left(xy\right)^2\right]^2\)
= \(\left(x^4y^4+1-x^2y^2\right)\left(x^4y^4+1+x^2y^2\right)\)
( mik ko bik đúng hay sai đâu nha) mik thấy nó thành nhân tử thì mik tách thôi
\(3x\left(x-5\right)-x\left(4+3x\right)=43\)
\(\Leftrightarrow3x^2-15x-4x-3x^2=43\)
\(\Leftrightarrow-19x=43\)
\(\Leftrightarrow x=\frac{-43}{19}\)
1)
\(6x^2+12xy+6y^2\)
\(=6(x^2+2xy+y^2)=6[(x^2+xy)+(xy+y^2)]\)
\(=6[x(x+y)+y(x+y)]=6(x+y)^2\)
2)
\(-3x^4y^2-6x^3y^2-3x^2y^3\)
\(=-3x^2y^2(x^2+2x+y)\)
3) \(-3x^4y-12x^2y-12x^2y\)
\(=-3x^4y-24x^2y\)
\(=-3x^2y(x^2+8)\)
4)
\(5x^4y^2+20x^3y^2+20x^2y^2\)
\(=5x^2y^2(x^2+4x+4)\)
\(=5x^2y^2[x^2+2x+2x+4]\)
\(=5x^2y^2[x(x+2)+2(x+2)]=5x^2y^2(x+2)^2\)
5)
\(4x^5y^2-8x^4y^2+4x^3y^2\)
\(=4x^3y^2(x^2-2x+1)\)
\(=4x^3y^2(x^2-x-x+1)\)
\(=4x^3y^2[x(x-1)-(x-1)]=4x^3y^2(x-1)^2\)