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a)x3-7x+6
=x3+0x2-7x+6
=x3-x2+x2-x-6x+6
=(x3-x2)+(x2-x)-(6x-6)
=x2(x-1)+x(x-1)-6(x-1)
=(x-1)(x2+x-6)
=(x-1)(x2-2x+3x-6)
=(x-1)[x(x-2)+3(x-2)]
=(x-1)(x+3)(x-2)
\(a,\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)
\(b,\left(6x^5y^2-9x^4y^3+15x^3y^4\right):3x^3y^2=2x^2-3xy+5y^2\)
\(c,\left(2x^3-21x^2+67x-60\right):\left(x-5\right)=\left(2x^3-10x^2-11x^2+55x+12x-60\right):x-5=\left[2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\right]:\left(x-5\right)=\left(x-5\right)\left(2x^2-11x+12\right)\left(x-5\right):\left(x-5\right)=2x^2-11x+12\)
a) (x3 + 8y3) : (2y + x)
= (x + 2y)(x2 - 2xy + 4y2) : (2y + x)
= x2 - 2xy + 4y2
b) (x3 + 3x2y + 3xy2 + y3) : (2x + 2y)
= (x + y)3 : 2(x + y)
= \(\dfrac{\left(x+y\right)^2}{2}\)
c) (6x5y2 - 9x4y3 + 15x3y4) : 3x3y2
= 3x3y2(2x2 - 3xy + 5y2) : 3x3y2
= 2x2 - 3xy + 5y2
a)\(\left(2x-y\right)[\left(2x\right)^2-2.2x.y+y^2]\)
\(=\left(2x-y\right)^3\)
b)\(2x^2-3xy+5y^2\)
c)\(2x^3-10x^2-11x^2+55x+12x-60\)
\(=2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\)
\(=\left(x+5\right)\left(2x^2-11x+12\right)\)
\(\Leftrightarrow(2x^3-21x^2+67x-60)/\left(x-5\right)=2x^2-11x+12\)
e, \(x^3+5x^2+8x+4=x^3+x^2+4x^2+4x+4x+4\)
\(=x^2\left(x+1\right)+4x\left(x+1\right)+4\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+4x+4\right)=\left(x+1\right)\left(x+2\right)^2\)
d, \(27x^3-27x^2+18x-4=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
a) (3x-1)(9x2+3x+1)=27x3-1
27x3-1=27x3-1
27x3-1-(27x3-1)=0
27x3-1-27x3+1=0
⇒x=0
b)(x2-5x+25)(x+5)=x3+125
(x+5)(x2-x.5+52)=x3+125
x3+125-(x3+125)=0
x3+125-x3-125=0
⇒x=0
c)(x-3)(x2-6x+9)=(x-3)3
x3-33-(x-3)3=0
x3-27-x3+27=0
⇒x=0
d) Đề phải là thế này chứ \(\left(x-y+4\right).\left(x-y-4\right)\)
\(=\left(x-y\right)^2-4^2\)
\(=\left(x-y\right)^2-16\)
\(=x^2-2.x.y+y^2-16\)
\(=x^2-2xy+y^2-16.\)
Chúc bạn học tốt!
mk ghi đáp án sau đó bạn tự biến đổi, không ra ib mk
a) \(x^3-9x^2+6x+16=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)
b) \(x^3-6x^2-x+30=\left(x-5\right)\left(x-3\right)\left(x+2\right)\)
c) \(2x^3-x^2+5x+3=\left(2x+1\right)\left(x^2-x+3\right)\)
mk làm tiếp
d) \(27x^3-27x^2+18x-4=\left(3x-1\right)\left(9x^2-6x+4\right)\)
e) \(x^2+2xy+y^2-x-y-12=\left(x+y-3\right)\left(x+y+4\right)\)
f) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)