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Y
17 tháng 6 2019
a) \(A=\left(x^2+x-2\right)\left(x+7\right)-16\)
\(=x^3+8x^2+5x-14-16\)
\(=x^3+8x^2+5x-30\)
\(=x^3+3x^2+5x^2+15x-10x-30\)
\(=x^2\left(x+3\right)+5x\left(x+3\right)-10\left(x+3\right)\)
\(=\left(x^2+5x-10\right)\left(x+3\right)\)
b) \(A=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)
\(=x^4-2x^3-2x^2+8\)
\(=x^3\left(x-2\right)-2\left(x^2-4\right)\)
\(=\left(x-2\right)\left(x^3-2x-4\right)\)
\(=\left(x-2\right)\left[x^2\left(x+2\right)+2x\left(x+2\right)-2\left(x+2\right)\right]\)
\(=\left(x-2\right)\left(x+2\right)\left(x^2+2x-2\right)\)
c) \(81x^4+4=81x^4+36x^2+4-36x^2\)
\(=\left(9x^2+2\right)^2-\left(6x\right)^2\)
\(=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)
d) \(\left(x^2-3\right)^2+16=x^4-6x^2+25\)
\(=\left(x^4+10x^2+25\right)-16x^2\)
\(=\left(x^2+5\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)
PT
2
18 tháng 6 2019
\(\left(x^2-x-2\right)^2+\left(x-2\right)^2\)
\(=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)
\(=x^4-2x^3-2x^2+8\)
\(=x^3\left(x-2\right)-2\left(x^2-4\right)\)
\(=x^3\left(x-2\right)-2\left(x-2\right)\left(x+2\right)\)
\(=\left(x-2\right)\left(x^3-2x-4\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\)
\(=\left(x-2\right)\left(x-2\right)\left(x^2+2x+2\right)\)
\(=\left(x-2\right)^2\left(x^2+2x+2\right)\)
Y
17 tháng 6 2019
a) \(=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)
\(=x^4-2x^3-2x^2+8\)
\(=x^3\left(x-2\right)-2x\left(x-2\right)-4\left(x-2\right)\)
\(=\left(x^3-2x-4\right)\left(x-2\right)\)
\(=\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\left(x-2\right)\)
\(=\left(x-2\right)^2\left(x^2+2x+2\right)\)
b) \(=x^4-x+2019\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right)+2019\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2019\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^2-x+2019\right)\)\
S
21 tháng 6 2019
\(\left(x^2-6x\right)^2-2\left(x-3\right)^2-81=\left[\left(x^2-6x\right)^2-81\right]-2\left(x-3\right)^2=\left[\left(x^2-6x\right)^2-9^2\right]-2\left(x-3\right)^2=\left(x^2-6x+9\right)\left(x^2-6x-9\right)-2\left(x-3\right)^2=\left(x-3\right)^2\left(x^2-6x-9\right)-2\left(x-3\right)^2=\left(x-3\right)^2\left(x^2-6x+11\right)\)
1 tháng 5 2019
1) x2-2xy+y2-x+y
(=) (x-y)2-(x-y)
(=) [(x-y)-1].(x-y)
(=) (x-y-1).(x-y)
C= (x-y)(x2+xy+y2)-x(x2-y)+y(y2-x)
(=) x3-y3-x3+xy+y3-xy
(=)(x3-x3)+(-y3+y3)+(xy-xy)
(=) 0
6 tháng 12 2022
\(=\dfrac{1}{4}\left(x-4y\right)\left(x^2+4xy+16y^2\right)+4\left(4y^3-\dfrac{1}{16}x^3+1\right)\)
\(=\dfrac{1}{4}\left(x^3-64y^3\right)+4\left(4y^3-\dfrac{1}{16}x^3+1\right)\)
\(=\dfrac{1}{4}x^3-16y^3+16y^3-\dfrac{1}{4}x^3+4=4\)
NT
2
24 tháng 8 2019
Giải giùm em \(\left(x^2+4x+8\right)^2+3x^3+14x^2+24x\) nha
S
24 tháng 8 2019
\(=\left(a-1\right)\left(a+4\right)\left(a+3\right)\left(a-2\right)-24=\left(a-2\right)\left(a+4\right)\left(a-1\right)\left(a+3\right)-24\)\(=\left(a^2+2a-8\right)\left(a^2+2a-3\right)-24.dat:a^2+2a-8=h\)\(\Rightarrow\left(a^2+2a-8\right)\left(a^2+2a-3\right)-24=h\left(h+5\right)-24=h^2+5h-24=\left(h-3\right)\left(h+8\right)\)\(=\left(a^2+2a-11\right)a\left(a+2\right)\)
S
28 tháng 6 2020
a) \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
Đặt \(x^2+x=t\), đa thức trở thành : \(t^2-2t-15\)
= \(\left(t+3\right)\left(t-5\right)\)
\(=\left(x^2+x+3\right)\left(x^2+x-5\right)\)
b) \(\left(a+b+c\right)^3-a^3-b^3-c^3\)
\(=a^3+b^3+c^3+2ab+2ac+2bc-a^3-b^3-c^3\)
\(=2ab+2ac+2bc=2\left(ab+ac+bc\right)\)
c) \(x-1+x^{n+3}-x^n\)
\(=x-1+x^n\left(x^3-1\right)\)
\(=x-1+x^n\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x-1\right)\left(x^{n+2}+x^{n+1}+x^n+1\right)\)
d) \(2x^4-7x^3-2x^2+13x+6\)
\(=\left(2x^4+2x^3\right)-\left(9x^3+9x^2\right)+\left(7x^2+7x\right)+\left(6x+6\right)\)
\(=\left(x+1\right)\left(2x^3-9x^2+7x+6\right)\)
\(=\left(x+1\right)\left[\left(2x^3+x^2\right)-\left(10x^2+5x\right)+\left(12x+6\right)\right]\)
\(=\left(x+1\right)\left(2x+1\right)\left(x^2-5x+6\right)\)
\(=\left(x+1\right)\left(2x+1\right)\left(x-2\right)\left(x-3\right)\)
\(x^4-6x^2+25=x^4+10x^2+25-16x^2\)
\(=\left(x^2+5\right)^2-\left(4x\right)^2=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)
\(=x^4-6x^2+25\)
\(=x^4+10x^2+25-16x^2\)
\(=\left(x^2+5\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)