Rút gọn (a-2b-3c-d).(a+2b+3c+d)
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Rút gọn:
(a+2b-3c-d)(a+2b+3c+d)
(1-x-2x3+3x2)(1-x+2x3-3x2)
a)(a+2b-3c-d)(a+2b+3c+d)=[(a+2b)-(3c+d)][(a+2b)+(3c-d)]
=(a+2b)2-(3c-d)2=a2+4ab+4b2-9c2+6cd-d2
câu b tương tự
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Rút gọn: (a + 2b - 3c - d)(a + 2b + 3c + d)
\(\left(a+2b-3c-d\right)\left(a+2b+3c+d\right)\)
\(=\left[\left(a+2b\right)-\left(3c-d\right)\right]\left[\left(a+2b\right)+\left(3c-d\right)\right]\)
\(=\left(a+2b\right)^2-\left(3c-d\right)^2\)
\(=a^2+4ab+4b^2-9c^2+6cd-d^2\)
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a, \(\left(a+2b-3c-d\right)\left(a+2b+3c+d\right)\)
\(=\left[\left(a+2b\right)-\left(3c+d\right)\right]\left[\left(a+2b\right)+\left(3c-d\right)\right]\)
\(=\left(a+2b\right)^2-\left(3c-d\right)^2=a^2+4ab-9c^2+6cd-d^2\)
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Cho 4 số thực a, b, c, d khác 0 thỏa mãn a+2b+3c+4d khác 0 và 3a+2b +3c+4d/a=a+6b+3c+4d/2b=a+2b+9c+4d/3c=a+2b+3c+12d/4a
cho a/b=c/d c/m 2a+3c/2a-3c=2b+3d/2b-3d
\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{2a}{2b}=\dfrac{3c}{3d}=\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)
\(\Rightarrow\dfrac{2a+3c}{2a-3c}=\dfrac{2b+3d}{2b-3d}\)
\(\Rightarrow dpcm\)
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rút gọn theo quy tắc đấu ngoặc
A =(a+b-2c) -(-a+b+c) -(2a-b-c)
B=-(2a-b+c) + (b-2c-3a) -(-5a-3c+b)
C=(3a-b-2c)-( 2b+3c-a) +(2a-3b)
D=(5a-3b+c) +( 2a-3b+5) -( b-c+a)
A =(a+b-2c) -(-a+b+c) -(2a-b-c)
= a+b-2c+a-b-c-2a+b+c
= b-2c
B=-(2a-b+c) + (b-2c-3a) -(-5a-3c+b)
= -2a+b-c+b-2c-3a+5a+3c-b
= b-c
C=(3a-b-2c)-( 2b+3c-a) +(2a-3b)
= a-b-2c-2b-3c+a+2a-3b
= -6b-5c
D=(5a-3b+c) +( 2a-3b+5) -( b-c+a)
= 5a-3b+c+2a-3b+5-b+c-a
= 6a-7b+2c
\(A=\left(a+b-2c\right)-\left(-a+b+c\right)-\left(2a-b-c\right)\)
\(=a+b-2c+a-b-c-2a+b+c=b-2c\)
\(B=-\left(2a-b+c\right)+\left(b-2c-3a\right)-\left(-5a-3c+b\right)\)
\(=-2a+b-c+b-2c-3a+5a+3c-b=b\)
\(C=\left(3a-b-2c\right)-\left(2b+3c-a\right)+\left(2a-3b\right)\)
\(=3a-b-2c-2b-3c+a+2a-3b=6a-6b-5c\)
\(D=\left(5a-3b+c\right)+\left(2a-3b+5\right)-\left(b-c+a\right)\)
\(=5a-3b+c+2a-3b+5-b+c-a=6a-7b+2c\)
sử dụng hằng đẳng thức đáng nhớ để thực hiện phép tính (a+2b-3c-d)(a+2b+3c+d)=?
help!
Ta có: \(\left(a+2b-3c-d\right)\left(a+2b+3c+d\right)\)
\(=\left[\left(a+2b\right)-\left(3c+d\right)\right]\cdot\left[\left(a+2b\right)+\left(3c+d\right)\right]\)
\(=\left(a+2b\right)^2-\left(3c+d\right)^2\)
\(=a^2+4ab+4b^2-9c^2-6cd-d^2\)
( a + 2b - 3c - d )( a + 2b + 3c + d )
= [ ( a + 2b ) - ( 3c + d ) ][ ( a + 2b ) + ( 3c + d ) ]
= ( a + 2b )2 - ( 3c + d )2
= a2 + 4ab + 4b2 - ( 9c2 + 6cd + d2 )
= a2 + 4ab + 4b2 - 9c2 - 6cd - d2
(a + 2b − 3c − d) (a + 2b + 3c + d)
= [(a + 2b) − (3c + d) ] · [(a + 2b) + (3c + d)]
= (a + 2b)2 − (3c + d)2
= a2 + 4ab + 4b2 − 9c2 − 6cd − d2
Hok tốt
bài 1:rút gọn
a)(a+1)(a+2)(a2+4)(a-1)(a2+1)(a-2)
b)(a+2b-3c-d)(a+2b+3c+d)
c)(1+x-2x3+3x2)(1-x+2x3-3x2)
d)(a6-3a3+9)(a2+3)
e)(a2-1)(a2-a+1)(a2+a+1)
8 tháng 8 2023 lúc 21:30
Cho \(\dfrac{2a+3c}{2b+3d}\)=\(\dfrac{2a-3c}{2b-3d}\). Chứng minh\(\dfrac{a}{b}\)=\(\dfrac{c}{d}\)
\(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}=\dfrac{2a+3c+2a-3c}{2b+3d+2b-3d}=\dfrac{a}{b}\)
\(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}=\dfrac{2a+3c-\left(2a-3c\right)}{2b+3d-\left(2b-3d\right)}=\dfrac{c}{d}\)
Suy ra \(\dfrac{a}{b}=\dfrac{c}{d}\)
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3 tháng 5 2023 lúc 20:31
Cho a/b=c/d Với b/d khác +-3/2 . Chứng minh rằng:
a)2a+3c/2b+3d=2a-3c/2b-3d.
b)a^2+c^2/b^2+d^2=ac/bd