Thu gọn biểu thức
B=-2a-5b+8a-10b-2b
C=-3c+10a-2b+10c-2a-2b+7c
Thu gọn biểu thức:
a) 2.( a-3b+5b) + (-3a-7c+5c) -4b b)7.(-a-2b+c)+3.(-2c-6b+a)
c)2.(-3c-6b+7b)-4.(2a-3b+8c) d) -3.(2a+3b-4c)+7.(-2c+8a-2c)+20a+2a+24b
e)-(5a-6b+c)+3.(-2c-6b+a)
rút gọn biểu thức :
(2a - 3b) - (5b - d) + (8b - d) = 2a
(a + b ) - (d - 4b ) - (c - 10d) = 2a - 2b - 6d +c
(2a-3b)-(5b-d)+(8b-d)
\(=2a-3b-5b+d+8b-d\)
\(=2a+\left(8b-3b-5b\right)+\left(d-d\right)\)
=2a
\(\left(a+b\right)-\left(d-4b\right)-\left(c-10d\right)\)
\(=a+b-d+4b-c+10d\)
\(=a+5b+11d-c\)
rút gọn:
a) \(\left(2a-5b\right)^2+\left(2a+5b\right)^2\)
b) \(\left(a-2b-3c\right)^2-\left(a-2b+3c\right)^2\)
Lời giải:
a)
\((2a-5b)^2+(2a+5b)^2\)
\(=4a^2-2.2a.5b+25b^2+4a^2+2.2a.5b+25b^2\)
\(=8a^2+50b^2=2(4a^2+25b^2)\)
b)
\((a-2b-3c)^2-(a-2b+3c)^2\)
\(=[(a-2b-3c)-(a-2b+3c)][(a-2b-3c)+(a-2b+3c)]\)
\(=-6c(2a-4b)=12c(2b-a)\)
Rút gọn các biểu thức câu a
(a+2b+3c)^2-2(a+2b+3c)*(2a+b)+(2a +b) ^2
Câub)(x-1)*(x+1 ) *(x^2+1)*(x^4+1)*(x^8+1)*(x^16+1)
a,(a+2b+3c)^2-2(a+2b+3c)*(2a+b)+(2a +b) ^2 = (a+2b+3c-2a-b)2
=(-a+b+3c)2
b,(x-1)*(x+1 ) *(x^2+1)*(x^4+1)*(x^8+1)*(x^16+1)=(x2-1)(x2+1)(x4-1)(x8+1)(x16+1)=(x4+1)(x4-1)(x8+1)(x16+1)=(x8-1)(x8+1)(x16+1)
=(x16-1)(x16+1)=x32-1
Bài 3: Thu gọn các biểu thức:
a) A=(2a+b+3c)-(a-b+c)
b) B= (a+b-c)-(a-b+c)-(a-b-c)
c) C=(a-2b-c)-(-2a+b-c)-(-a-b-2c)
\(a,A=\left(2a+b+3c\right)-\left(a-b+c\right)\)
\(=2a+b+3c-a+b-c\)
\(=a+2b-2c\)
\(b,B=\left(a+b-c\right)-\left(-2a+b-c\right)-\left(-a-b-2c\right)\)
\(=a+b-c+2a-b+c+a+b+2c\)
\(=4a+b+2c\)
\(c,C=\left(a-2b-c\right)-\left(-2a+b-c\right)-\left(-a-b-2c\right)\)
\(=a-2b-c+2a-b+c+a+b+2c\)
\(=4a-2b+2c\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}\). Chứng minh:
1) \(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)
2) \(\dfrac{4a-3b}{4c-3d}=\dfrac{4a+3b}{4c+3d}\)
3) \(\dfrac{3a+5b}{3a-5b}=\dfrac{3c+5d}{3c-5d}\)
4) \(\dfrac{3a-7b}{b}=\dfrac{3c-7d}{d}\)
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: \(\dfrac{3a-7b}{b}=\dfrac{3c-7d}{d}\)
cho các số a,b,c thỏa mãn 3a-2b/4=2c-4a/3=4b-3c/2 tính giá trị biểu thức A=3a+2b-c/3a-2b+c + 2a^2-b^2+c^2/2a^2+b^2-c^2
làm ơn trả lời hộ mk với ah mai mk phải nộp bài r
CMR
-(-4a+5c-3b)-(2b-a+7c)+(-7b+3c-5a)=-9c-6b
-(2a-3c+b)+(-5b-4c+12a)-(-9b-4c+4a)+(-6a-3b-3c)+d=d
phá ngoặc lun nà
+4a-5c+3b-2b+a-7c-7b+3c-5a=(4a+a-5a)+(3b-2b-7b)+(-5c-7c+3c)=0-6b-9c=-9c-6b
-2a+3c-b-5b-4c+12a+9b+4c-4a-6a-3b-3c+d=(-2a+12a-4a-6a)+(-b-5b+9b-3b)+(3c-4c+4c-3c)+d=0+0+0+0+d=d
Tính giá trị của các biểu thức sau A=\(\dfrac{2a-5b}{a-3b}-\dfrac{4a+b}{8a-2b}\)biết \(\dfrac{a}{b}=\dfrac{3}{4}\)
\(\dfrac{a}{b}=\dfrac{3}{4}\Leftrightarrow\dfrac{a}{3}=\dfrac{b}{4}=\dfrac{2a-5b}{-14}=\dfrac{a-3b}{-9}=\dfrac{4a+b}{16}=\dfrac{8a-2b}{16}\\ \Leftrightarrow A=\dfrac{-14}{-9}-\dfrac{16}{16}=\dfrac{14}{9}-1=\dfrac{5}{9}\)