Question

Chứng minh rằng

a, \(\left(2n-3\right).n-2n.\left(n+2\right)⋮7\forall n\in Z\)

b, \(n.\left(2n-3\right)-2n.\left(n+1\right)⋮5\forall n\in Z\)

Rút gọn

a, (3x-5) . (2x+11) - (2x+3) . (3x+7)

b, (x+2) . (2x²-3x+4) - (x²-1) . (2x+1)

c, 3x² .(x²+2) + 4x. (x²-1) - (x²+2x+3) . (3x²-2x+1)

Answer 1

\(a,\left(2x-3\right)n-2n\left(n+2\right)\)

\(=n\left(2x-3-2n-4\right)\)

\(=-7n\)

Vì \(-7⋮7\Rightarrow-7n⋮7\) => ĐPCM

\(b,n\left(2n-3\right)-2n\left(n+1\right)\)

\(=n\left(2n-3-2n-2\right)\)

\(=-5n⋮5\) (ĐPCM)

Rút gọn

\(a,\left(3x-5\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)\)

\(=6x^2+33x-10x-55-6x^2-14x-9x-21\)

\(=-76\)

\(b,\left(x+2\right)\left(2x^2-3x+4\right)-\left(x^2-1\right)\left(2x+1\right)\)

\(=2x^3-3x^2+4x+4x^2-6x+8-2x^3-x^2+2x+1\)

\(=9\)

\(c,3x^2\left(x^2+2\right)+4x\left(x^2-1\right)-\left(x^2+2x+3\right)\left(3x^2-2x+1\right)\)

\(=3x^4+6x^2+4x^3-4x-3x^4+2x^3-x^2-6x^3+4x^2-2x-9x^2+6x-3\)

= -3