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1: \(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)
=(x^2+x)^2+3(x^2+x)-10
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)
2: \(=\left(x^2+5ax+4a^2\right)\left(x^2+5ax+6a^2\right)+a^4\)
\(=\left(x^2+5ax\right)^2+10a^2\left(x^2+5ax\right)+25a^2\)
\(=\left(x^2+5ax+5a^2\right)^2\)
3: \(=\left(a+b\right)^3+c^3-3ab\left(a+b\right)-3abc\)
\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)
5: \(M=\left(n+1\right)\left(n^2+2n\right)+360\)
=n(n+1)(n+2)+360 chia hết cho 6
6A
7D
Ta có: x 2 (x + 1) − x(x + 1) = (x + 1).( x 2 – x)
= (x+ 1).x (x-1) = x.(x- 1).(x+ 1)
Chọn D. x(x − 1)(x + 1).
Bài 1 yêu cầu gì em?
Bài 2:
\(a,x\left(x-1\right)+5\left(x-1\right)=\left(x+5\right)\left(x-1\right)\\ b,3x\left(x+1\right)+3\left(x+1\right)=\left(3x+3\right)\left(x+1\right)=3\left(x+1\right)\left(x+1\right)=3\left(x+1\right)^2\\ c,x\left(x-3\right)+xy\left(x-3\right)=\left(x+xy\right)\left(x-3\right)=x\left(y+1\right)\left(x-3\right)\\ d,2x\left(x-2\right)-6\left(x-2\right)=\left(2x-6\right)\left(x-2\right)=2\left(x-3\right)\left(x-2\right)\)
Bài 1:
a) \(3xy+6y\)
\(=3y\left(x+2\right)\)
b) \(3x^2+9x\)
\(=3x\left(x+3\right)\)
c) \(6x-9y^2\)
\(=3\left(2x-3y^2\right)\)
d) \(10xy^2-6x^2y\)
\(=2xy\left(5y-3x\right)\)
Bài 2:
a) \(x\left(x-1\right)+5\left(x-1\right)\)
\(=\left(x-1\right)\left(x+5\right)\)
b) \(3x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(3x+3\right)\)
\(=3\left(x+1\right)\left(x+1\right)\)
\(=3\left(x+1\right)^2\)
c) \(x\left(x-3\right)+xy\left(x-3\right)\)
\(=\left(x+xy\right)\left(x-3\right)\)
\(=x\left(1+y\right)\left(x-3\right)\)
d) \(2x\left(x-2\right)-6\left(x-2\right)\)
\(=\left(2x-6\right)\left(x-2\right)\)
\(=2\left(x-3\right)\left(x-2\right)\)
A
A