bạn ghi lại đề đi bạn

làm ơn trả lời hộ mk với ah mai mk phải nộp bài r

a,=(2a + b - 3c).(2a + b - 3c)

=4a\(^2\)+2ab-6ac+2ab+b\(^2\)-3bc-6ac-3cb+9c\(^2\)

=4a\(^2\)+b\(^2\)+9c\(^2\)+4ab

=2\(^2\).a\(^2\)+4ab+b\(^2\)+9c\(^2\)

=(2a+b)\(^2\)+9c\(^2\)( đáng lẽ chỗ này nó phải là -9c\(^2\) nhưng t ko ra đc )

b,=(a + 2b + 3c - 4d)(a + 2b + 3c - 4d)

=a\(^2\)+2ab+3ac-4ad+2ab+4b\(^2\)+6bc-8bd+3ac+6bc+9c\(^2\)-12cd-4ad-8bd-12cd+16d\(^2\)

=a\(^2\)+4b\(^2\)+9c\(^2\)+16d\(^2\)+4ab+6ac-8ad+12bc-16bd-24cd

=(a\(^2\)+4ab+4b\(^2\))+(9c\(^2\)-24cd+16d\(^2\))+6ac-8ad+12bc-16bd

=(a+2b)\(^2\)+(3c-4d)\(^2\)+2(3ac-4ad+6bc-8bd)

=(a+2b)\(^2\)+(3c-4d)\(^2\)+2[a(3c-4d)+2b(3c-4d)]

=(a+2b)\(^2\)+(3c-4d)\(^2\)+2(a+2b)(3c-4d)

khiếp bài dài nghoằng ra ý :(

a: \(\left(2a+b-3c\right)^2\)

\(=4a^2+b^2+9c^2+4ab-12ac-6bc\)

đặt a/b =c/d =k 

=> a=bm , c=dm 

=> 2a+3c/2b+3d =2bm+3bm/ 2b +3d = m.(2d+3d)/2d+3d =m (1)

=> 2a-3c/2d-3d=2bm-3dm /2b -3d =m.(2b-3d)/2b-3d= m (2)

Từ (1) và (2) => 2a+3c/2b+3d =2a-3c/2b-3d 

câu 2 tương tự nha

bạn khôi đặt là k mà lại khi m

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=>\(a=bk;c=dk\)

1: \(\dfrac{2a+3c}{2b+3d}=\dfrac{2\cdot bk+3\cdot dk}{2b+3d}=\dfrac{k\left(2b+3d\right)}{2b+3d}=k\)

\(\dfrac{2a-3c}{2b-3d}=\dfrac{2bk-3dk}{2b-3d}=\dfrac{k\left(2b-3d\right)}{2b-3d}=k\)

Do đó: \(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)

2: \(\dfrac{4a-3b}{4c-3d}=\dfrac{4\cdot bk-3b}{4\cdot dk-3d}=\dfrac{b\left(4k-3\right)}{d\left(4k-3\right)}=\dfrac{b}{d}\)

\(\dfrac{4a+3b}{4c+3d}=\dfrac{4bk+3b}{4dk+3d}=\dfrac{b\left(4k+3\right)}{d\left(4k+3\right)}=\dfrac{b}{d}\)

Do đó: \(\dfrac{4a-3b}{4c-3d}=\dfrac{4a+3b}{4c+3d}\)

3: \(\dfrac{3a+5b}{3a-5b}=\dfrac{3bk+5b}{3bk-5b}=\dfrac{b\left(3k+5\right)}{b\left(3k-5\right)}=\dfrac{3k+5}{3k-5}\)

\(\dfrac{3c+5d}{3c-5d}=\dfrac{3dk+5d}{3dk-5d}=\dfrac{d\left(3k+5\right)}{d\left(3k-5\right)}=\dfrac{3k+5}{3k-5}\)

Do đó: \(\dfrac{3a+5b}{3a-5b}=\dfrac{3c+5d}{3c-5d}\)

4: \(\dfrac{3a-7b}{b}=\dfrac{3bk-7b}{b}=\dfrac{b\left(3k-7\right)}{b}=3k-7\)

\(\dfrac{3c-7d}{d}=\dfrac{3dk-7d}{d}=\dfrac{d\left(3k-7\right)}{d}=3k-7\)

Do đó: \(\dfrac{3a-7b}{b}=\dfrac{3c-7d}{d}\)

a) Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)

Khi đó (2a + 3c)(2b - 3d) 

= (2bk + 3dk)(2b - 3d)

= k(2b + 3d)(2b - 3d) (1)

(2a - 3c)(2b + 3d)

= (2bk - 2dk)(2b + 3d)

= k(2b - 3d)(2b + 3d) (2)

Từ (1)(2) => (2a + 3c)(2b - 3d) = (2a - 3c)(2b + 3d)

b) Sửa đề (4a + 3b)(4c - 3d) = (4a - 3b)(4c + 3d) 

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)

Ta có (4a + 3b)(4c - 3d) = (4bk + 3b)(4dk - 3d) = bd(4k + 3)(4k - 3) (1)

Lại có (4a - 3b)(4c + 3d) = (4bk - 3b)(3dk + 3d) = bd(4k- 3)(4k + 3) (2)

Từ (1)(2) => (4a + 3b)(4c - 3d) = (4a - 3b)(4c + 3d) 

1, Ta có: \(\frac{a}{b}=\frac{c}{d}\)

\(\Rightarrow\frac{2a}{2b}=\frac{3c}{3d}=\frac{2a+3c}{2b+3d}=\frac{2a-3c}{2b-3d}\)

\(\Rightarrow\left(2a+3c\right).\left(2b-3d\right)=\left(2a-3c\right).\left(2b+3d\right)\)

        Vậy (2a + 3c).(2b - 3d) = (2a - 3c).(2b + 3d)

Câu 2 cũng tương tự nên tự làm đi