2x^2+4x+xy+2y
x^2+xy-7x-7y
ac+bc+a+b
7z^2-7yz-4z+4y
x^3+3x^2+3x+9
pq-p^2-5(p-q)
phân tích các đa thức thành nhân tử y^2+1+2y-49
36a^2-c^-9b^2-6bc
ab(a-b)+b^2c-bc^2+c^2a-ca^2
2x^2+4x+xy+2y x^2+xy-7x-7y ac+bc+a+b 7z^2-7yz-4z+4y x^3+3x^2+3x+9 pq-p^2-5(p-q) phân tích các đa thức thành nhân tử y^2+1+2y-49 36a^2-c^-9b^2-6bc ab(a
By Ariana
`1)2x^2+4x+xy+2y`
`=(2x^2+4x)+(xy+2y)`
`=2x(x+2)+y(x+2)`
`=(x+2)(2x+y)`
`2)x^2+xy-7x-7y`
`=(x^2+xy)-(7x+7y)`
`=x(x+y)-7(x+y)`
`=(x+y)(x-7)`
`3)ac+bc+a+b`
`=(ac+bc)+(a+b)`
`=c(a+b)+(a+b)`
`=(a+b)(c+1)`
`4)7z^2-7yz-4z+4y`
`=(7z^2-7yz)-(4z-4y)`
`=7z(z-y)-4(z-y)`
`=(z-y)(7z-4)`
`5)x^3+3x^2+3x+9`
`=(x^3+3x^2)+(3x+9)`
`=x^2(x+3)+3(x+3)`
`=(x+3)(x^2+3)`
`6)pq-p^2-5(p-q)`
`=(pq-p^2)-5(p-q)`
`=p(q-p)-5(p-q)`
`=-p(p-q)-5(p-q)`
`=(p-q)(-p-5)`
`7)y^2+1+2y-49`
`=(y^2+2y+1)-7^2`
`=(y+1)^2-7^2`
`=(y+1+7)(y+1-7)`
`=(y+8)(y-6)`
`8)36a^2-c^2-9b^2-6bc`
`=(6a)^2-(c^2+6bc+9b^2)`
`=(6a)^2-(c+3b)^2`
`=(6a+c+3b)(6a-c-3b)`
`9)ab(a-b)+b^2c-bc^2+c^2a-ca^2`
`=ab(a-b)+(b^2c-ca^2)+(c^2a-bc^2)`
`=ab(a-b)-c(a^2-b^2)+c^2(a-b)`
`=ab(a-b)-c(a-b)(a+b)+c^2(a-b)`
`=(a-b)(ab-ac-bc+c^2)`
`=(a-b)[(ab-ac)-(bc-c^2)]`
`=(a-b)[a(b-c)-c(b-c)]`
`=(a-b)(b-c)(a-c)`
$(2x^2+4x+xy+2y)$
=$2x(x+2)+y(x+2)$
=$(x+2)(2x+y)$
$(x^2+xy-7x-7y)$
=$x(x+y)-7(x+y)$
=$(x+y)(x-7)$
$(ac+bc+a+b)$
=$c(a+b)+(a+b)$
=$(a+b)(c+1)$
$(7z^2-7yz-4z+4y)$
=$7z(z-y)-4(z-y)$
=$(z-y)(7z-4)$
$(x^3+3x^2+3x+9)$
=$x^2(x+3)+3(x+3)$
=$(x+3)(x^2+3)$
$(pq-p^2-5(p-q))$
=$p(q-p)+5(q-p)$
=$(q-p)(p+5)$
$(y^2+1+2y-49)$
=$(y^2+2y+1)-49$
=$(y+1)^2-7^2$
=$(y+1-7)(y+1+7)$
=$(y-6)(y+8)$
$(36a^2-c^2-9b^2-6bc)$
=$[(6a)^2-(c^2+6bc+9b^2)$
=$[(6a)^2-(c+3b)^2]$
=$(6a-3b-c)(6a+3b+c)$
$(ab(a-b)+b^2c-bc^2+c^2a-ca^2($
=$a^2b-ab^2+b^2c-bc^2+c^2a-ca^2$
=$(a^2b-bc^2)+(-ab^2+b^2c)+(c^2a-ca^2)$
=$b(a^2-c^2)-b^2(a-c)-ca(a-c)$
=$b(a-c)(a+c)-b^2(a-c)-ca(a-c)$
=$(a-c)(ab+bc-b^2-ca)$
=$(a-c)[(ab-b^2)+(bc-ca)]$
=$(a-c)[b(a-b)-c(a-b)]$
=$(a-b)(b-c)(a-c)$