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\(x^2-9x+8\)
\(=x^2-8x-x+8\)
\(=x.\left(x-8\right)-\left(x-8\right)\)
\(=\left(x-8\right).\left(x-1\right)\)
\(x^2+6x+8\)
\(=x^2+4x+2x+8\)
\(=x.\left(x+4\right)+2.\left(x+4\right)\)
\(=\left(x+2\right).\left(x+4\right)\)
P/S: mk chỉ bt làm 2 bài này thôi =)
a) \(2x^2-4xy+2y^2-32\)
\(=2\left(x^2-2xy+y^2-16\right)\)
\(=2\left[\left(x-y\right)^2-4^2\right]\)
\(=2\left(x-y-4\right)\left(x-y+4\right)\)
b) \(5x^2-5y^2-x+y\)
\(=5\left(x^2-y^2\right)-\left(x-y\right)\)
\(=5\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left[5\left(x+y\right)-1\right]\)
\(=\left(x-y\right)\left(5x+5y-1\right)\)
c) \(x^2-9x+8\)
\(=x^2-x-8x+8\)
\(=x\left(x-1\right)-8\left(x-1\right)\)
\(=\left(x-1\right)\left(x-8\right)\)
d) \(x^2+6x+8\)
\(=x^2+2x+4x+8\)
\(=x\left(x+2\right)+4\left(x+2\right)\)
\(=\left(x+2\right)\left(x+4\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
Bài làm
a) 3x2 - 6x2 + 3x
= -3x2 + 3x
= 3x( 1 - x )
b) 3x2 + 5x - 3xy - 5y
= ( 3x2 - 3xy ) + ( 5x - 5y )
= 3x( x - y ) + 5( x - y )
= ( x - y )( 3x + 5 )
c) x3 + 2x2 + x
= x( x2 + 2x + 1 )
= x( x2 + 2.x.1 + 12 )
= x( x + 1 )2
d) xy + y2 - x - y
= ( xy - x ) + ( y2 - y )
= x( y - 1 ) + y( y - 1 )
= ( y - 1 )( x + y )
# Học tốt #
mk viết đáp án, ko biết biến đổi ib mk
a) \(x^3+3x^2y-9xy^2+5y^3=\left(x+5y\right)\left(x-y\right)^2\)
b) \(x^4+x^3+6x^2+5x+5=\left(x^2+5\right)\left(x^2+x+1\right)\)
c) \(x^4-2x^3-12x^2+12x+36=\left(x^2-6\right)\left(x^2-2x-6\right)\)
d) \(x^8y^8+x^4y^4+1=\left(x^2y^2-xy+1\right)\left(x^2y^2+xy+1\right)\left(x^4y^4-x^2y^2+1\right)\)
a, x2-7x-14y+2x
=x(x+2)-7(x-2y)
b, x3-4x2y+4xy2-25x
=x3-4x2y+4xy2-y3-25x+y3
=(x-y)3-25x+y3
a ) = x(x+2) - 7(x+2y)
b) = -4 xy ( x-y) + (x^3-25x) [ câu này mk , chaqcs là làm đúng đâu ]
a) (x2-4x+3)(x2-10x+24)+8=((x2-x)-(3x-3))((x2-6x)-(4x-24))+8
=(x(x-1)-3(x-1))(x(x-6)-4(x-6))+8=(x-1)(x-3)(x-4)(x-6)+8=((x-1)(x-6))(x-3)(x-4))+8
=(x2-7x+6)(x2-7x+12)+8
Đặt x2-7x+6=a
Ta có : a(a+6)+8=a2+6a+8=(a+2)(a+4)=(x2-7x+8)(x2-7x+10)=(x2-7x+8)(x-5)(x-2)
b) Tương tự như câu a kết quả là (x-3)(x3+9x2+21x+9)
c) x4+x3+6x2+3x+9=(x4+x3+3x2)+(3x2+3x+9)=x2(x2+x+3)+3(x2+x+3)=(x2+x+3)(x2+2)
\(x^8y^8+x^4y^4+1=\left[\left(x^4y^4\right)^2+2x^4y^4+1\right]-x^4y^4=\left(x^4y^4+1\right)^2-\left(x^2y^2\right)^2\)
\(=\left(x^4y^4+1-x^2y^2\right)\left(x^4y^4+1+x^2y^2\right)\)
\(=\left(x^4y^4+1-x^2y^2\right)\left[\left(x^2y^2\right)^2+2x^2y^2+1-x^2y^2\right]\)
\(=\left(x^4y^4+1-x^2y^2\right)\left[\left(x^2y^2+1\right)^2-\left(xy\right)^2\right]\)
\(=\left(x^4y^4+1-x^2y^2\right)\left(x^2y^2+1-xy\right)\left(x^2y^2+1+xy\right)\)
Phân tích đa thức thành nhân tử
x3+3x2y−9xy2+5y2
x8y8+x4y4+1
\(x^2-y^2+6x+9=\left(x+3\right)^2-y^2=\left(x+3+y\right)\left(x+3-y\right)\)
\(x^3+3x^2-9x-27=\left(x-3\right)\left(x^2+3x+9\right)+3x\left(x-3\right)=\left(x-3\right)\left(x^2+6x+9\right)=\left(x-3\right)\left(x+3\right)^2\)