Question

BT4: Cho hai đa thức \(A=\left(\dfrac{1}{3}a-\dfrac{1}{3}b\right)-\left(a-2b\right)\) và \(B=\dfrac{1}{3}a-\dfrac{1}{3}b-\left(a-b\right)\)

Tính A+B và A-B

Answer 1

\(+\) Rút gọn \(A,B\)

\(A=\left(\dfrac{1}{3}a-\dfrac{1}{3}b\right)-\left(a-2b\right)\)

\(=\dfrac{1}{3}a-\dfrac{1}{3}b-a+2b\)

\(=\left(\dfrac{1}{3}a-a\right)+\left(2b-\dfrac{1}{3}b\right)\)

\(=-\dfrac{2}{3}a+\dfrac{5}{3}b\)

\(B=\dfrac{1}{3}a-\dfrac{1}{3}b-\left(a-b\right)\)

\(=\dfrac{1}{3}a-\dfrac{1}{3}b-a+b\)

\(=\left(\dfrac{1}{3}a-a\right)+\left(b-\dfrac{1}{3}b\right)\)

\(=-\dfrac{2}{3}a+\dfrac{2}{3}b\)

\(+\) Tính \(A+B\)

\(A+B=-\dfrac{2}{3}a+\dfrac{5}{3}b-\dfrac{2}{3}a+\dfrac{2}{3}b\)

\(=\left(-\dfrac{2}{3}a-\dfrac{2}{3}a\right)+\left(\dfrac{5}{3}b+\dfrac{2}{3}b\right)\)
\(=-\dfrac{4}{3}a+\dfrac{7}{3}b\)

\(+\) Tính \(A-B\)

\(A-B=\left(-\dfrac{2}{3}a+\dfrac{5}{3}b\right)-\left(-\dfrac{2}{3}a+\dfrac{2}{3}b\right)\)

\(=-\dfrac{2}{3}a+\dfrac{5}{3}b+\dfrac{2}{3}a-\dfrac{2}{3}b\)

\(=\left(-\dfrac{2}{3}a+\dfrac{2}{3}a\right)+\left(\dfrac{5}{3}b-\dfrac{2}{3}b\right)\)

\(=0+\dfrac{3}{3}b\)

\(=b\)

 

Answer 2

\(A=\left(\dfrac{1}{3}a-\dfrac{1}{3}b\right)-\left(a-2b\right)\\ A=\dfrac{1}{3}a-\dfrac{1}{3}b-a+2b\\ A=-\dfrac{2}{3}a+\dfrac{5}{3}b\\ \\ \)

\(B=\dfrac{1}{3}a-\dfrac{1}{3}b-\left(a-b\right)\\ B=\dfrac{1}{3}a-\dfrac{1}{3}b-a+b\\ B=-\dfrac{2}{3}a+\dfrac{2}{3}b\\ B=\dfrac{2}{3}\left(-a+b\right) \)
 

\(A+B=-\dfrac{2}{3}a+\dfrac{5}{3}b+\left(-\dfrac{2}{3}a+\dfrac{2}{3}b\right)\\ A+B=-\dfrac{2}{3}a+\dfrac{5}{3}b-\dfrac{2}{3}a+\dfrac{2}{3}b\\ A+B=-\dfrac{4}{3}a+\dfrac{7}{3}b\)

\(A-B=-\dfrac{2}{3}a+\dfrac{5}{3}b-\left(-\dfrac{2}{3}a+\dfrac{2}{3}b\right)\\ A-B=-\dfrac{2}{3}a+\dfrac{5}{3}b+\dfrac{2}{3}a-\dfrac{2}{3}b\\ A-B=\dfrac{5}{3}b-\dfrac{2}{3}b\\ A-B=b\)