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a) (2x+y)3
c)(x2-y2)(x4+x2y2+y4)
d)-x3+9x2-27x+27
<=> -(x3-9x2+27x-27)
<=>-(x-3)3
b)3x^2-18x+27=3x^2-9x-9x+27=3x*(x-3)-9*(x-3)=(x-3)*(3x-9)=(x-3)*3*(x-3)=3*(x-3)^2
c)x^3-4x^2-12x+27=(x+3)*(x^2-3x+9-4)=(x+3)*(x^2-3x+5)
d)27x^3-1/27=(3x-1/3)*(9x^2-x+1/9) (hang dt)
con a) voi e) mk chiu
\(1,4x^4+4x^2y^2-8y^4\)
\(=4\left(x^4+x^2y^2-y^4-y^4\right)\)
\(=4\left[\left(x^4-y^4\right)+\left(x^2y^2-y^4\right)\right]\)
\(=4\left[\left(x^2+y^2\right)\left(x^2-y^2\right)+y^2\left(x^2-y^2\right)\right]\)
\(=4\left(x^2-y^2\right)\left(x^2+y^2+y^2\right)\)
\(=4\left(x-y\right)\left(x+y\right)\left(x^2+2y^2\right)\)
\(2,12x^2y-18xy^2-30y^3\)
\(=6y\left(2x^2-3xy-5y^2\right)\)
\(=6y\left[\left(2x^2+2xy\right)-\left(5xy+5y^2\right)\right]\)
\(=6y\left[2x\left(x+y\right)-5y\left(x+y\right)\right]\)
\(=6y\left(x+y\right)\left(2x-5y\right)\)
a) \(4x^2-8x+4-9\left(x-y\right)^2\)
\(=4\left(x^2-2x+1\right)-9\left(x-y\right)^2\)
\(=\left[2\left(x-1\right)\right]^2-\left[3\left(x-y\right)\right]^2\)
\(=\left(2x-2+3x-3y\right)\left(2x-2-3x+3y\right)\)
\(=\left(5x-3y-2\right)\left(3y-x-2\right)\)
b) \(x^3-4x^2+12x-27\)
\(=\left(x^3-27\right)-\left(4x^2-12x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right)-4x\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2-x+9\right)\)
tớ lm câu a thui nha , tại khó quá ^^
a/ \(=3x^6+3x^5+6x^4+3x^3+3x^2-7x^5-7x^4-14x^3-7x^2-7x+3x^4+3x^3+6x^2+3x+1\)
\(=3x^2\left(x^4+x^3+2x^2+x+1\right)-7x\left(x^4+x^3+2x^2+x+1\right)+3\left(x^4+x^3+2x^2+x+1\right)\)
\(=\left(3x^2-7x+3\right)\left(x^4+x^3+x^2+x^2+x+1\right)\)
\(=\left(3x^2-7x+3\right)\left[x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\right]\)
\(=\left(3x^2-7x+3\right)\left(x^2+1\right)\left(x^2+x+1\right)\)
1) \(x^6+1\)
\(=x^6+x^4-x^4+x^2-x^2+1\)
\(=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)
\(=x^2\left(x^4-x^2+1\right)+\left(x^4-x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
2) \(x^6-y^6\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)\left(x-y\right)\left(x^2+xy+y^2\right)\)
a, \(\left(4x+5\right)^2=\left(4x+5\right)\left(4x+5\right)=\left[\left(4x+5\right)4x\right]+\left[\left(4x+5\right)5\right]=4x^2+20x+25\)
b, \(\left(5x-2\right)^2=\left(5x-2\right)\left(5x-2\right)=\left[\left(5x-2\right)5x-\left(5x-2\right)2\right]=5x^2-10x+25\)
b, \(8^2-12x^2=\left(8^2-12x^2\right)\left(8^2+12x^2\right)\)
đúng ko :)
@No name: Bị sai rồi nhé, a,b,c sai hết :>
a) ( 4x + 5 )2
= ( 4x )2 + 2.4x.5 + 52
= 16x2 + 40x + 25
b) ( 5x - 2 )2
= ( 5x )2 - 2.5x.2 + 22
= 25x2 - 20x + 4
c) 82 - 12x2
= 64 - 12x2
= ( V8 - V12x )( V8 + V12x )
\(a,8x^3+12x^2y+6xy^2+y^3=\left(2x\right)^3+3.\left(2x\right)^2.y+3.2x.y^2+y^3=\left(2x+y\right)^3\)
\(b,x^2-9=x^2-3^2=\left(x-3\right)\left(x+3\right)\)
\(c,4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)
CÁC BẠN ƠI CHỖ KIA LÀ 1/27 NHÉ MIK VIẾT NHẦM
a) 4x4 - 4x2y + y2 = ( 2x - y )2
b) 8x6 - 1/27 = ( 2x2 )3 - ( 1/3 )3 = ( 2x2 - 1/3 )( 4x4 + 2/3x2 + 1/9 )
c) x4 - y4 = ( x2 )2 - ( y2 )2 = ( x2 - y2 )( x2 + y2 ) = ( x + y )( x - y )( x2 + y2 )
d) 1 + 6x2 + 12x4 + 8x6 = ( 2x2 + 1 )3