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Đặt x2+10x+5=a.Ta có biểu thức là : a(a+8)+16=a2+8a+16=(a+4)2=(x2+10x+9)2
\(x^2-y^2+10x-6y+16\)
\(=\left(x^2+10x+25\right)-\left(y^2+6y+9\right)\)
\(=\left(x+5\right)^2-\left(y+3\right)^2\)
\(=\left(x+5-y-3\right)\left(x+5+y+3\right)\)
\(=\left(x-y+2\right)\left(x+y+8\right)\)
Ta có \(x^4+10x^3+32x^2+40x+16=\left(x^4+2x^3\right)+\left(8x^3+16x^2\right)+\left(16x^2+32x\right)+\left(8x+16\right)\)
\(=x^3\left(x+2\right)+8x^2\left(x+2\right)+16x\left(x+2\right)+8\left(x+2\right)\)
\(=\left(x+2\right)\left(x^3+8x^2+16x+8\right)=\left(x+2\right)\left(x+2\right)\left(x^2+6x+4\right)\)
\(=\left(x+2\right)^2\left(x^2+6x+4\right)\)
x^2-y^2+10x-6y+16=(x^2-10x+25)-(y^2+6y+9)=(x-5)^2-(y+3)^2=(x-5-y-3)(x-5+y+3)=(x-y-8)(x+y-2)
\(x^2-10x+16\)
\(=\left(x^2-2x\right)-\left(8x-16\right)\)
\(=x.\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x-8\right)\)
Tham khảo nhé~
phân tích đa thức thành nhân tử
a, 6x^2 + 7xy + 2y^2
=6x^2+3xy+4xy+2y^2
=3x(x+y)+2y(x+y)
=(3x+2y)(x+y)
b, 9x^2 - 9xy - 4y^2
=9x^2 +3xy-12xy-4y^2
=3x(x+y)-4y(x+y)
=(3x+4y)(x+y)
c, x^2 - y^2 + 10x - 6y + 16=x^2-y^2+6x-6y+4x+16=x(x+6)-y(x+6)+4(x+6)=(x-y+4)(x+6)
Bài làm
a, 6x2 + 7xy + 2y2
= 6x2 + 3xy + 4xy + 2y2
= ( 6x2 + 3xy ) + ( 4xy + 2y2 )
= 3x( 2x + y ) + 2y( 2x + y )
= ( 2x + y )( 3x + 2y )
b, 9x2 - 9xy - 4y2
= 9x2 - 12xy + 3xy - 4y2
= ( 9x2 - 12xy ) + ( 3xy - 4y2 )
= 3x( 3x - 4y ) + y ( 3x - 4y )
= ( 3x + y )( 3x - 4y )
c, x2 - y2 + 10x - 6y + 16
= x2 - y2 - 6x + 6y + 4x + 16
= x( x + 6 ) - y( x + 6 ) + 4( x + 6 )
= ( x - y + 4 )( x + 6 )
# Học tốt #
a) 8x2-2x-1=8x2+4x-2x-2x-1=(8x2+4x)-(2x+1)=4x.(2x+1)-(2x+1)=(2x+1).(4x-1)
b) x2-y2+10x-6y+16x=x2-y2+10x+10y-16y+16x=(x-y)(x+y)+10(x+y)-16(y+x)=(x+y)(x-y+10+16)
\(x^2-10x+16\)
\(=x^2-2x-8x+16\)
\(=x\left(x-2\right)-8\left(x-2\right)=\left(x-2\right)\left(x-8\right)\)
\(x^2-8x+15\)
\(=x^2-3x-5x+15\)
\(=x\left(x-3\right)-5\left(x-3\right)=\left(x-3\right)\left(x-5\right)\)
c) x2 -10x + 16
= x2 - 2x - 8x + 16
= x.(x-2) - 8.(x-2)
= (x-2).(x-8)
d) x2 - 8x + 15
= x2 - 3x - 5x + 15
= x.(x-3) - 5.(x-3)
= (x-3).(x-5)
\(=x^2+2x+8x+16\)
\(=x\cdot\left(x+2\right)+8\cdot\left(x+2\right)\)
\(=\left(x+2\right)\cdot\left(x+8\right)\)