## 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

Question

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

in progress 0
3 tuần 2021-07-08T17:20:31+00:00 2 Answers 3 views 0

1. 1)2x²+4x+xy+2y

=(2x²+4x)+(xy+2y)

=2x(x+2)+y(x+2)

=(x+2)(2x+y)

2)x²+xy-7x-7y

=(x²+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)7z²-7yz-4z+4y

=(7z²-7yz)-(4z-4y)

=7z(z-y)-4(z-y)

=(z-y)(7z-4)

5)x³+3x²+3x+9

=(x³+3x²)+(3x+9)

=x²(x+3)+3(x+3)

=(x+3)(x²+3)

6)pq-p²-5(p-q)

=(pq-p²)-5(p-q)

=p(q-p)+5(q-p)

=(q-p)(p+5)

7)y²+1+2y-49

=(y²+2y+1)-49

=(y+1)²-7²

=(y+1+7)(y+1-7)

=(y+8)(y-6)

8)36a²-c²-9b²-6bc

=(6a)²-(9b²+6bc+c²)

=(6a)²-[(3b)²+2.3b.c+c²]

=(6a)²-(3b+c)²

=(6a-3b-c)(6a-3b+c)

9)ab(a-b)+b²c-bc²+c²a-ca²

=a²b-ab²+b²c-bc²+c²a-ca²

=(c²a-bc²)+(b²c-ca²)+(a²b-ab²)

=c²(a-b)+c(b²-a²)+ab(a-b)

=c²(a-b)-c(a²-b²)+ab(a-b)

=c²(a-b)-c(a+b)(a-b)+ab(a-b)

=(a-b)[c²-c(a+b)+ab]

=(a-b)(c²-ac-bc+ab)

=(a-b)[(c²-bc)-(ac-ab)]

=(a-b)[c(c-b)-a(c-b)]

=(a-b)(c-b)(c-a)

2. $(2x^2+4x+xy+2y)$

=$2x(x+2)+y(x+2)$

=$(x+2)(2x+y)$

$(x^2+xy-7x-7y)$

=$x(x+y)-7(x+y)$

=$(x+y)(x-7)$

$(ac+bc+a+b)$

=$c(a+b)+(a+b)$

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

$(7z^2-7yz-4z+4y)$

=$7z(z-y)-4(z-y)$

=$(z-y)(7z-4)$

$(x^3+3x^2+3x+9)$

=$x^2(x+3)+3(x+3)$

=$(x+3)(x^2+3)$

$(pq-p^2-5(p-q))$

=$p(q-p)+5(q-p)$

=$(q-p)(p+5)$

$(y^2+1+2y-49)$

=$(y^2+2y+1)-49$

=$(y+1)^2-7^2$

=$(y+1-7)(y+1+7)$

=$(y-6)(y+8)$

$(36a^2-c^2-9b^2-6bc)$

=$[(6a)^2-(c^2+6bc+9b^2)$

=$[(6a)^2-(c+3b)^2]$

=$(6a-3b-c)(6a+3b+c)$

$(ab(a-b)+b^2c-bc^2+c^2a-ca^2($

=$a^2b-ab^2+b^2c-bc^2+c^2a-ca^2$

=$(a^2b-bc^2)+(-ab^2+b^2c)+(c^2a-ca^2)$

=$b(a^2-c^2)-b^2(a-c)-ca(a-c)$

=$b(a-c)(a+c)-b^2(a-c)-ca(a-c)$

=$(a-c)(ab+bc-b^2-ca)$

=$(a-c)[(ab-b^2)+(bc-ca)]$

=$(a-c)[b(a-b)-c(a-b)]$

=$(a-b)(b-c)(a-c)$