Question

Answer 1

Bài 8:

a: Đặt \(A=a\left(a-1\right)-\left(a+3\right)\left(a+2\right)\)

\(=a^2-a-\left(a^2+5a+6\right)\)

\(=a^2-a-a^2-5a-6=-6a-6=-6\left(a+1\right)\)

=>A⋮6

b: Đặt \(B=a\left(a+2\right)-\left(a-5\right)\left(a-7\right)\)

\(=a^2+2a-\left(a^2-12a+35\right)\)

\(=a^2+2a-a^2+12a-35=14a-35=7\left(2a-5\right)\)

=>B⋮7

c: Đặt \(C=\left(n^2-3n+1\right)\left(n+2\right)-n^3+n^2+3\)

\(=n^3+2n^2-3n^2-6n+n+2-n^3+n^2+3\)

=-5n+5

=5(-n+1)⋮5

Bài 1:

a: (x+2)(x-3)

\(=x^2-3x+2x-6\)

\(=x^2-x-6\)

b: \(\left(x^2-1\right)\left(x+2\right)=x^3+2x^2-x-2\)

c: \(\left(x^2+2x\right)\left(x^2-1\right)\)

\(=x^2\cdot x^2-x^2\cdot1+2x\cdot x^2-2x\cdot1\)

\(=x^4+2x^3-x^2-2x\)

d: \(\left(x+1\right)\left(x^2-x+1\right)\)

\(=x^3-x^2+x+x^2-x+1\)

\(=x^3+1\)

e: \(\left(x^2-2x+3\right)\left(x-4\right)\)

\(=x^3-4x^2-2x^2+8x+3x-12\)

\(=x^3-6x^2+11x-12\)