Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a.x\(^6\)-y\(^6\)=(x\(^2\))\(^3\)+(y\(^2\))\(^3\) =(x\(^2\)+y\(^2\))(x\(^4\)-x\(^2\)y\(^2\)+y\(^4\))
b.x\(^{35}\)+x\(^{34}\)+......+x+1 =x\(^{34}\).(x+1)+......+(x+1)
=(x\(^{34}\)+x\(^{32}\)+......+x\(^2\)+1)(x+1)
c.x\(^2\)-6xy+9y\(^2\)-9 =x\(^2\)-2.3xy+(3y)\(^2\)-3\(^2\) =(x-3y)\(^2\)-3\(^2\)
=(x-3y-3)(x-3y+3)
d.(x-9)(x-7)+1 =x\(^2\)-7x-9x+63+1 =x\(^2\)-16x+64
=x\(^2\)-2.8x+8\(^2\) =(x-8)\(^2\)
a) \(\left(x-9\right)\left(x-7\right)+1\)
\(=x^2-16x+63+1\)
\(=x^2-16x+64\)
\(=\left(x-8\right)^2\)
b) \(x^3+2x^2-3x-6\)
\(=x^2\left(x+2\right)-3x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-3x\right)\)
\(=x\left(x+2\right)\left(x-3\right)\)
c) \(x^2-y^2+xz-yz\)
\(=x\left(x+z\right)-y\left(y+z\right)\)
\(=\left(x-y\right)\left(y+z\right)\)
d) \(x^3-x+3x^2y+y^3-y\)
botay:(
a) 7(x-y)
b) (x-3y)2
c) xy(x+y)-(x+y)=(xy-1)(x+y)
d) x2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)
\(a,x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right).\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right).\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(b,9x^2+y^2+6xy=\left(3x\right)^2+2.3x.y+y^2=\left(3x+y\right)^2\)
\(c,6x-9-x^2=-\left(x^2-6x+9\right)=-\left(x^2-2.x.3+3^2\right)=-\left(x-3\right)^2\)
a)\(x^2-6xy+9y^2=x^2-2\cdot x\cdot3y+\left(3y\right)^2=\left(x-3y\right)^2\)
b) \(\left(x^2+1\right)^2-4x^2\)
\(=\left(x^2+1+2x\right)\left(x^2+1-2x\right)\)
\(=\left(x+1\right)^2\left(x-1\right)^2\)
Ta có : x35 + x34 + x33 +.......+ x2 + x + 1
= (x35 + x34 ) + (x33 + x32) +.......+ (x3 + x2) + (x + 1)
= x34(x + 1) + x32(x + 1) + .... + x2(x + 1) + (x + 1)
= (x + 1) ( x34 + x32 + ..... + x2 + 1)
Ta có : (x - 9)(x - 7) + 1
= x2 - 16x + 63 + 1
= x2 - 16x + 64
= x2 - 2.x.8 + 82
= (x - 8)2