a) ko biết làm ! SORRY

b) ( a + b ) . ( a + b )

= \(\left(a+b\right)^2\)

c) ( a - b ) . ( a - b )

= \(\left(a-b\right)^2\)

Học tốt nhé !

\(\frac{2}{2.6}\)+\(\frac{3}{6.10}\)+ \(\frac{3}{10.14}\)+...+ \(\frac{3}{26.30}\)

=\(\frac{2}{12}\)+ \(\left(\frac{3.4}{4.6.10}+\frac{3.4}{4.10.14}+...+\frac{3.4}{4.26.30}\right)\)

= \(\frac{2}{12}\)+ \(\frac{3}{4}\). \(\left(\frac{4}{6.10}+\frac{4}{10.14}+...+\frac{4}{26.30}\right)\)

= \(\frac{2}{12}\)+ \(\frac{3}{4}\). \(\left(\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{30}\right)\)

= \(\frac{2}{12}\)+ \(\frac{3}{4}\).\(\left(\frac{1}{6}-\frac{1}{30}\right)\)

= \(\frac{2}{12}\)+ \(\frac{3}{4}\). \(\left(\frac{5}{30}-\frac{1}{30}\right)\)

= \(\frac{2}{12}\)+ \(\frac{3}{4}\). \(\frac{4}{30}\)

= \(\frac{2}{12}\)+ \(\frac{1}{1}\). \(\frac{1}{10}\)

= \(\frac{2}{12}\)+ \(\frac{1}{10}\)

= \(\frac{10}{60}\)+ \(\frac{6}{60}\)

= \(\frac{16}{60}\)= \(\frac{4}{15}\)

 Chúc bạn học tốt nhé !

\(a.\left(b-c\right)-b.\left(a+c\right)\)

\(=ab-ac-ab+bc\)

\(=\left(ab-ab\right)-ac+bc\)

\(=-ac+bc\)

\(=bc-ac\)

\(a.\left(b-c\right)-b.\left(a+c\right)\)

\(=ab-ac-ab-bc\)

\(=\left(ab-ab\right)-\left(ac+bc\right)\)

\(=-\left(a+b\right)c\)

a, Ta có

\(\hept{\begin{cases}42⋮7\\56⋮7\end{cases}\Rightarrow42+56⋮7}\)

b, Ta có

\(\hept{\begin{cases}140⋮7\\49⋮7\end{cases}\Rightarrow140-49⋮7}\)

Ta có :

+) a ≡ 10 ( mod 15 ) mà 15 ⁝ 3 

=> a ≡ 10 ( mod 3 )

=> a ≡ 1 ( mod 3 )

=> a chia 3 dư 1 => a ⁒ 3

+) a ≡ 10 ( mod 15 ) mà 15 ⁝ 5

=> a ≡ 10 ( mod 5 )

=> a ≡ 0 ( mod 5 )

=> a chia 5 dư 0

=> a ⁝ 5

Từ \(\hept{\begin{cases}a⋮m\\b⋮m\end{cases}\Rightarrow\hept{\begin{cases}k_1a⋮m\\k_2b⋮m\end{cases}\Rightarrow}k_1a+k_2b⋮m}\)

vì a chia hết cho m suy ra k₁a chia hết cho m (1)

vì b chia hết cho m suy ra k_2b chia hết cho m (2)

từ (1),(2) suy ra k₁a + k₂b\(⋮\)m

\(a⋮m\Rightarrow k_1a⋮m\)

\(b⋮m\Rightarrow k_2b⋮m\)

\(\Rightarrow k_1a+k_2b⋮m\)

Gọi số quyển vở là x; sô bút là y ta có

\(15000x+7000y=265000\)

\(\Rightarrow15x+7y=265\)

\(\Rightarrow7y=265-15x=259-14x+6-x\)

\(7y⋮7\Rightarrow259-14x+6-x⋮7\)

\(259-14x⋮7\Rightarrow6-x⋮7\Rightarrow x=6\)

\(\Rightarrow y=25\)