a) \(4x^4-21x^2y^2+y^4=\left(4x^4+4x^2y^2+y^4\right)-25x^2y^2\)
\(=\left(2x^2+y^2\right)^2-\left(5xy\right)^2=\left(2x^2-5xy+y^2\right)\left(2x^2+5xy+y^2\right)\)
b) \(x^5-5x^3+4x=x\left(x^4-5x^2+4\right)=x\left[\left(x^4-4x^2\right)-\left(x^2-4\right)\right]\)
\(=x\left[x^2\left(x^2-4\right)-\left(x^2-4\right)\right]=x\left(x^2-1\right)\left(x^2-4\right)\)
\(=x\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)\)
c ) \(x^3+5x^2+3x-9=\left(x^3-x^2\right)+\left(6x^2-6x\right)+\left(9x-9\right)\)
\(=x^2\left(x-1\right)+6x\left(x-1\right)+9\left(x-1\right)\)
\(=\left(x^2+6x+9\right)\left(x-1\right)=\left(x+3\right)^2\left(x-1\right)\)
d ) \(x^{16}+x^8-2=x^{16}-x^8+2x^8-2=x^8\left(x^8-1\right)+2\left(x^8-1\right)\)
\(=\left(x^8+2\right)\left(x^8-1\right)=\left(x^8+2\right)\left(x^4-1\right)\left(x^4+1\right)\)
\(=\left(x^8+2\right)\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)=\left(x^8+2\right)\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\left(x^4+1\right)\)
e ) \(x^3-11x^2+30x=0\)
\(\Leftrightarrow x\left(x^2-11x+30\right)=0\)
\(\Leftrightarrow x\left[\left(x^2-5x\right)-\left(6x-30\right)\right]=0\)
\(\Leftrightarrow x\left[x\left(x-5\right)-6\left(x-5\right)\right]=0\)
\(\Leftrightarrow x\left(x-6\right)\left(x-5\right)=0\)
\(\Rightarrow x=0orx=5orx=6\) (or hoặc)
Vậy \(x\in\left\{0;5;6\right\}\)
a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
1.
= 4x\(^{^{ }2}\)-4x-9x+9
=4x(x-1)-9(x-1)
=(4x-9)(x-1)
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)
bạn hỏi từng câu 1 lần thôi cũng đc hỏi 1 lần 17 câu thì thánh nào vô kiên nhẫn trả lời hết đc ^^
a: \(=7x^3\left(1-2xy+3x^2y^2\right)\)
b: \(=x\left(x-y\right)+11\left(x-y\right)=\left(x-y\right)\left(x+11\right)\)
c: \(=4\left(x-3\right)\left(x+3\right)\)
d: \(=\left(x+3\right)^2-4y^2=\left(x+3+2y\right)\left(x+3-2y\right)\)
e: \(=xy\left(x+1\right)+z\left(x+1\right)=\left(x+1\right)\left(xy+z\right)\)
f: \(=\left(x-y\right)\left(x+y\right)-6\left(x-y\right)=\left(x-y\right)\left(x+y-6\right)\)
i) x3- 11x2 + 30x
=\(x\left(x^2-11x+30\right)\)
=\(x\left(x-6\right)\left(x-5\right)\)
j) 4x4- 21x2y2 + y4
=4x^4+4x^2y^2+y^4-25x^2y^2
=(2x^2+y^2)^2-(5xy)^2
=(2x^2+y^2-5xy)(2x^2+y^2+5xy)
k,x3 + 4x2- 7x - 10
i: \(x^3-11x^2+30x\)
\(=x\left(x^2-11x+30\right)\)
\(=x\left(x-6\right)\left(x-5\right)\)
j: \(4x^4-21x^2y^2+y^4\)
\(=\left(2x^2+y^2\right)^2-25x^2y^2\)
\(=\left(2x^2-5xy+y^2\right)\left(2x^2+5xy+y^2\right)\)
k: \(x^3+4x^2-7x-10\)
\(=x^3+5x^2-x^2-5x-2x-10\)
\(=\left(x+5\right)\cdot\left(x^2-x-2\right)\)
\(=\left(x+5\right)\left(x-2\right)\left(x+1\right)\)
i) x3- 11x2 + 30x
=x( x2-11x+30)
=x(x2-5x-6x+30)
=x[x(x-5)-6(x-5)]
=x(x-5)(x-6)
K)x3+4x2−7x−10x3+4x2−7x−10
=x3−2x2+6x2−12x+5x−10=x3−2x2+6x2−12x+5x−10
=x2(x−2)+6x(x−2)+5(x−2)=x2(x−2)+6x(x−2)+5(x−2)
=(x−2)(x2+6x+5)=(x−2)(x2+6x+5)
=(x−2)(x2+x+5x+5
Đúng(0)
L)x2+x)2−2(x2+x)−15(x2+x)2−2(x2+x)−15
=(x2+x)2−2(x2+x)+1−16=(x2+x)2−2(x2+x)+1−16
=(x2+x−1)2−42=(x2+x−1)2−42
=(x2+x−1+4)(x2+x−1−4)=(x2+x−1+4)(x2+x−1−4)
=(x2+x+3)(
Đúng(0)
l: Ta có: \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)^2-5\left(x^2+x\right)+3\left(x^2+x\right)-15\)
\(=\left(x^2+x-5\right)\left(x^2+x+3\right)\)