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\(B=m^2-mn+m-n^2-n+mn\\ B=m^2+m-n^2-n\\ B=\left(\dfrac{-2}{3}\right)^2-\dfrac{2}{3}-\left(\dfrac{-1}{3}\right)^2+\dfrac{1}{3}\\ B=\dfrac{4}{9}-\dfrac{2}{3}-\dfrac{1}{9}+\dfrac{1}{3}=0\)
\(B=m\left(m-n+1\right)-n\left(n+1-m\right)=m\left(m+n+1-2n\right)-n\left(m+n+1-2m\right)=\left(m+n\right)\left(m+n+1\right)-2mn+2mn=\left(m+n\right)\left(\dfrac{-2}{3}-\dfrac{1}{3}+1\right)-4mn=0-0=0\)
\(B=m^2-mn+m-n^2-n+mn=m^2-n^2+n-n\\ =\left(m-n\right)\left(m+n+1\right)\\ =\left(-\dfrac{2}{3}+\dfrac{1}{3}\right)\left(-\dfrac{2}{3}-\dfrac{1}{3}+1\right)=-\dfrac{1}{3}\cdot0=0\)
\(B=m\left(m-n+1\right)-n\left(n+1-m\right)=m^2-mn+m-n^2-n+mn=m^2-n^2+m-n=\left(m-n\right)\left(m+n\right)+\left(m-n\right)=\left(m-n\right)\left(m+n+1\right)=\left(-\dfrac{2}{3}+\dfrac{1}{3}\right)\left(-\dfrac{2}{3}-\dfrac{1}{3}+1\right)=-\dfrac{1}{3}.0=0\)
B = m(m - n + 1) - n(n + 1 - m)
B = m2 - mn + m - n2 - n + mn
B = m2 + m - mn + mn - n2 - n
B = m2 + m - n2 - n
Thay \(m=-\dfrac{2}{3};n=-\dfrac{1}{3}\), ta được:
B =\(\left(-\dfrac{2}{3}\right)^2+\left(-\dfrac{2}{3}\right)-\left(-\dfrac{1}{3}\right)^2-\left(-\dfrac{1}{3}\right)\)
B = \(\dfrac{4}{9}-\dfrac{2}{3}-\dfrac{1}{9}+\dfrac{1}{3}\)
B = \(\dfrac{3}{9}-\dfrac{1}{3}\)
B = \(\dfrac{1}{3}-\dfrac{1}{3}=0\)
a) 2n^3 + 2n^2 - 2n^3 - 2n^2 + 6n = 6n chia hết 6
b) 3n - 2n^2 - ( n + 4n^2 - 1 - 4n ) - 1
= 3n - 2n^2 - n - 4n^2 + 1 + 4n -1
= 6n - 6n^2 chia hết 6
c) m^3 + 8 - m^3 + m^2 - 9 - m^2 - 18
= - 19
Bài 1:
\(2n^2\left(n+1\right)-2n\left(n^2+n-3\right)\)
\(=2n\left(n^2+n-n^2-n+3\right)\)
\(=6n\)\(⋮\)\(6\)
Bài 2:
\(n\left(3-2n\right)-\left(n-1\right)\left(1+4n\right)-1\)
\(=3n-2n^2-\left(n+4n^2-1-4n\right)-1\)
\(=6n-6n^2=6\left(n-n^2\right)\)\(⋮\)\(6\)
Bài 3:
\(\left(m^2-2m+4\right)\left(m+2\right)-m^3+\left(m+3\right)\left(m-3\right)-m^2-18\)
\(=m^3+8-m^3+m^2-9-m^2-18\)
\(=-19\)
\(\Rightarrow\)đpcm
Lần sau bạn lưu ý ghi đề thì ghi cho thật đầy đủ yêu cầu của nó nhé.
Tính B.
Lời giải:
$m=\frac{-2}{3}; n=\frac{-1}{3}\Rightarrow m+n+1=0$
$B=m(m-n+1)-n(n+1-m)=m^2-mn+m-n^2-n+mn$
$=m^2-n^2+m-n=(m-n)(m+n+1)=(m-n).0=0$