Question

phân tích da thức sau thành nhân tử :

a) -25x⁶ -y⁸ +10x³y⁴

b) 49(y-4)²-9(y+2)²

c) x²+2xy+y²-xz-yz

d)1+(a+b+c)+(ab+bc+ca)+abc

Answer 1

a)

\(-25x^6-y^8+10x^3y^4=-(25x^6+y^8-10x^3y^4)\)

\(=-[(5x^3)^2-2.5x^3y^4+(y^4)^2]\)

\(=-(5x^3-y^4)^2\)

b) \(49(y-4)^2-9(y+2)^2=7^2(y-4)^2-3^2(y+2)^2\)

\(=(7y-28)^2-(3y+6)^2=(7y-28-3y-6)(7y-28+3y+6)\)

\(=(4y-34)(10y-22)=4(2y-17)(5y-11)\)

Answer 2

c)

\(x^2+2xy+y^2-xz-yz=(x^2+2xy+y^2)-(xz+yz)\)

\(=(x+y)^2-z(x+y)=(x+y)(x+y-z)\)

d)

\(1+(a+b+c)+(ab+bc+ac)+abc\)

\(=(1+a+b+ab)+(bc+ac+abc+c)\)

\(=(1+a+b+ab)+c(b+a+ab+1)\)

\(=(a+b+ab+1)(c+1)\)

\(=[(a+ab)+(b+1)](c+1)\)

\(=[a(b+1)+(b+1)](c+1)\)

\(=(a+1)(b+1)(c+1)\)