= 2( a^3 + b^3 ) + 7ab(a+b) = 2(a+b)(a^2 -ab +b^2)  + 7ab(a+b)  = (a+b) ( 2a^2 - 2ab + 2b^2 - 7ab)

=(a +b ) ( 2a^2 +2b^2 - 9ab)

saj ruj thang Tran saj

\(P = 2a^3 + 7a^2b + 7ab^2 + 2b^3\)

\(=2a^3+2a^2b+5a^2b+5ab^2+2ab^2+2b^3\)

\(=2a^2(a+b)+5ab(a+b)+2b^2(a+b) \)

\(=(2a^2+5ab+2b^2)(a+b)\)

\(=(2a^2+4ab+ab+2b^2)(a+b)\)

\(=[2a(a+2b)+b(a+2b)](a+b)\)

\(=(2a+b)(2b+a)(a+b)\)

P=2a³+7a²b+7ab²+2b³

=2a³+2a²b+5a²b+5ab²+2ab²+2b²

=(2a³+2a²b)+(5a²b+5ab²)+(2ab²+2b³)

=2a²(a+b)+5ab(a+b)+2b²(a+b)

=(a+b)(2a²+5ab+2b²)

=(a+b)[2a²+4ab+ab+2b²]

=(a+b)[2a(a+2b)+b(a+2b)]

=(a+b)(2a+b)(a+2b)

à. so easy

\(P=2a^3+7a^2b+7ab^2+2b^3\)

\(P=2a^3+2a^2b+5a^2b+5ab^2+2ab^2+2b^3\)

\(P=\left(2a^3+2a^2b\right)+\left(5a^2b+5ab^2\right)+\left(2ab^2+2b^3\right)\)

\(P=2a^2\left(a+b\right)+5ab\left(a+b\right)+2b^2\left(a+b\right)\)

\(P=\left(a+b\right)\left(2a^2+5ab+2b^2\right)\)

\(P=\left(a+b\right)\left[2a^2+4ab+ab+2b^2\right]\)

\(P=\left(a+b\right)\left[2a\left(a+2b\right)+b\left(a+2b\right)\right]\)

\(P=\left(a+b\right)\left(2a+b\right)\left(a+2b\right)\)

`a^2 + ab + 2a + 2b = a(a+2) + b(a+2) = (a+b)(a+2)`

2a²b²+2b²c²+2a²c²-a⁴-b⁴-c⁴

=4a²c²-(a⁴+b⁴+c⁴-2a²b²+2a²c²-2b²c²)

=4a²c²-(a²-b²+c²)²

=(2ac+a²-b²+c²)(2ac-a²+b²-c²)

=[(a+c)²-b²][b²-(a-c)²]

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

a) x⁴+x³+2x²+x+1=(x⁴+x³+x²)+(x²+x+1)=x²(x²+x+1)+(x²+x+1)=(x²+x+1)(x²+1)

b)a³+b³+c³-3abc=a³+3ab(a+b)+b³+c³ -(3ab(a+b)+3abc)=(a+b)³+c³-3ab(a+b+c)

=(a+b+c)((a+b)²-(a+b)c+c²)-3ab(a+b+c)=(a+b+c)(a²+2ab+b²-ac-ab+c²-3ab)=(a+b+c)(a²+b²+c²-ab-ac-bc)

c)Đặt x-y=a;y-z=b;z-x=c

a+b+c=x-y-z+z-x=o

đưa về như bài b

d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung

e)x²(y-z)+y²(z-x)+z²(x-y)=x²(y-z)-y²((y-z)+(x-y))+z²(x-y)

=x²(y-z)-y²(y-z)-y²(x-y)+z²(x-y)=(y-z)(x²-y²)-(x-y)(y²-z²)=(y-z)(x²-2y²+xy+xz+yz)

ko bik

Gọi a+b =x có:  

a(x+b)³−b(x+a)³

 =a(x³+3x²b+3xb²+b³)−b(x³+3x²a+3xa²+a³)  

=ax³+3ax²b+3axb²+ab³−bx³−3bx²a−3bxa²−ba³  

=(a−b)x³+(3ax²b−3bx²a)+(3axb²−3bxa²)+ab³−ba³  

=(a−b)x³+3axb(b−a)+ab(b²−a²)  

=−x³(b−a)+3axb(b−a)+ab(b+a)(b−a)

 =−x³(b−a)+3axb(b−a)+(a²b+ab²)(b−a)

 =(b−a)(−x³+3axb+a²b+ab²)

nho lik e

a^4+b^4+c^4-2a^2b^2+2b^2c^2-2a^2c^2-4b^2c^2

=(a^2-b^2-c^2)-4b^2c^2

=(a^2-b^2-c^2-2bc)(a^2-b^2-c^2+2bc)

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

a⁴+b⁴+c⁴- 2a²b²- 2b²c²- 2c²a²

= (a²-b²-c²)²