\(a.64x^4+y^4\\ =\left(8x^2\right)^2+\left(y^2\right)^2+16x^2y^2-16x^2y^2\\ =\left(8x^2+y^2\right)^2-\left(4xy\right)^2\\= \left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
\(b.a^6+a^4+a^2b^2+b^4-b^6\\ =\left(a^2\right)^3-\left(b^2\right)^3+a^4+a^2b^2+b^4\\ =\left(a^2-b^2\right)\left(a^4+a^2b^2+b^4\right)+a^4+a^2b^2+b^4\\ =\left(a^2-b^2+1\right)\left(a^4+a^2b^2+b^4\right)\)
\(c.x^3+3xy+y^3-1\\= x^3+3x^2y+3xy^2+y^3-1-3x^2y-3xy^2+3xy\\ =\left(x+y\right)^3-1-3xy\left(x+y-1\right)\\ =\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\\ =\left(x+y-1\right)\left(x^2+y^2+2xy-3xy+x+y+1\right)\\= \left(x+y-1\right)\left(x^2+y^2-xy+x+y+1\right)\)
\(d.4x^4+4x^3+5x^2+2x+1\\ =4x^4+2x^3+2x^3+2x^2+2x^2+x^2+x+x+1\\ =\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\\ =2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\\ =\left(2x^2+x+1\right)\left(2x^2+x+1\right)\\ =\left(2x^2+x+1\right)^2\)
\(e.x^8+x+1\\= x^8+x^7-x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+1\\ =\left(x^8+x^7+x^6\right)-\left(x^7+x^6+x^5\right)+\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\\ =\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
Mình làm tắt.
a) 64x4 + y4
= (8x2)2 + 16x2y2 + (y2)2 - 16x2y2
= 8x2+y2)2 - (4xy)2
= (8x2 + y2 + 4xy)(8x2 + y2- 4xy)
b) a6 + a4 + a2b2 + b4 - b6
= (a6-b6) + (a4 + a2b2 + b4)
= (a2 - b2)(a4 + a2b2 b4) + (a4 + a2b2 + b4)
= (a2 - b2 + 1)(a4 + a2b2 + b4)
c) x3 + 3xy + y3 - 1
= (x3 + 3x2y + 3xy2 + y2-1)- 3x2y -3xy2 + 3xy
= [ (x+y)3 - 1] - 3xy(x+y-1)
=(x + y -1)(x2 + 2xy + y2 + x + y + 1 - 3xy)
= (x + y - 1)(x2 - xy + y2 + x + y + 1)
d) 4x4 + 4x3 + 5x2 + 2x + 1
= 4x4 + 4x3 + x2 + 4x2 + 2x + 1
= (2x2+x)2 + (2x + 1)2
= x(2x + 1)2 + (2x + 1)2
= (x+1) (2x+1)2
e) x8 + x+ 1
= x8 - x5 + x5 - x2 + x2 +x +1
= x5(x3 - 1) + x2(x3- 1) + (x2 + x + 1)
= x5(x -1)(x2 + x + 1) + x2(x - 1)(x2+x+1) + (x2+x+1)
=(x2 + x + 1)(x6 - x5 + x3 - x2 + 1)
