1. Rút gọn các biểu thức sau:
a) (a+b)^2-(a-b)^2
b) (a+b)^3-(a-b)^3-2b^3
c) (x+y+z)^2-2(x+y+z)(x+y)+(x+y)^2
a) (x+y+z)^2 - 2(x+y+z)(x+y)+(x+y)^2
b) (a+b)^3 - (a - b)^3 - 2b^3
c) (a + b)^2 - (a - b)^2
a)(x+y+z)2 - 2(x+y+z)(x+y)+(x+y)2
=[(x+y+z)-(x-y)]2
=(x+y+z-x-y)2
=z2
b) (a+b)3 - (a - b)3 - 2b3
=[(a+b)-(a-b)][(a+b)2+(a+b)(a-b)+(a-b)2]-2b3
=(a+b-a+b)(a2+2ab+b2+a2-b2+a2-2ab+b2)-2b3
=2b(3a2+b2)-2b3
=6a2b+2b3-2b3
=6a2b
c) (a + b)2 - (a - b)2=[a+b+(a-b)][a+b-(a-b)]=(a+b+a-b)(a+b-a+b)
=2a.2b=4ab
Rút gọn biểu thức sau
(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2
2.Tính
a)(2+xy)^2
b) (5-3x)^2
c) (5-x^2)(5+x^2)
d) (5x-1)^3
e) (2x-y)(4x^2+2xy+y^2)
3.Rút gọn các biểu thức sau:
a) (a+b)^2 -(a-b)^2
b) (a+b)^3 -(a-b)^3-2b^3
c) (x+y+z)^2 -2(x+y+z)(x+y)+(x+y)^2
P/s:giúp mình giải nhé!!! giải theo 7 hằng đẳng thức đáng nhớ.
Bài 1:
a,(2+xy)^2=4+4xy+x^2y^2b,(5-3x)^2=25-30x+9x^2d,(5x-1)^3=125x^3 - 75x^2 + 15x^2 - 1Rút gọn các biểu thức sau :
a) (a + b) 2 - (a - b) 2
b) (a + b) 3 - (a - b) 3 - 2b 3
c) (x + y + z) 2 - 2.(x + y + z).(x + y) + (x + y) 2
a, ( a+ b + a - b)(a + b - a + b )
= 2a . 2b
= 4ab
c, = (x + y + z - x - y )2 = z2
a)
(a + b + a – b) (a + b – a + b)
= 2a . 2b
= 4ab
b) = a3 + 3a2b + 3ab2 + b3 - ( a3 - 3a2b + 3ab2 -b3)-2b3
= a3 + 3a2b + 3ab2 + b3 - a3 + 3a2b - 3ab2 + b3-2b3
= 6a2b
a) = a2 + 2ab + b2 - ( a2 - 2ab + b2)
= a2 + 2ab + b2 - a2 + 2ab - b2
= 4ab
Rút gọn các biểu thức sau:
a) (a+b)2 - (a - b)2
b) (a+b)3 - (a - b)3 - 2b3
c) (x+y+z)2 - 2(x+y+z)(x+y) + ( x+ y )2
Bài 1 : Rút gọn các biểu thức sau :
a) (a +b )2 - ( a -b )2
b) (a + b )3 - ( a - b )3 - 2b3
c) ( x+y+z)2 - 2(x+y+z)(x+y) + (x + y )2
Bài 2 : Tính giá trị biểu thức :
a) x2 + 4x + 4 tại x = 98
b) x3 + 3x2 + 3x +1 tại x=99
Bài 1:
a) \(\left(a+b\right)^2-\left(a-b\right)^2\)
\(=\left(a+b+\left(a-b\right)\right).\left(a+b-\left(a-b\right)\right)\)
\(=2a.2b\)
\(=4ab\)
Câu 1:
a) (a +b )2 - ( a -b )2
=a2+b2-a2+b2
=2b2
b) (a + b )3- ( a - b )3 - 2b3
=a3+b3-a+b3-2b3
=a3-a
c) ( x+y+z)2 - 2(x+y+z)(x+y) + (x + y )2
=x2+xy+xz+xy+y2+yz+xz+yz+z2-2.(x2+xy+xz+xy+y2+yz)+x2+xy+xy+y2
=x2+y2+z2+2xy+2xz+2yz-2x2-2y2-4xy-2xz-2yz+x2+2xy+y2
=0
Câu 2:
a) x2 + 4x + 4
Tại x = 98 ta có:
982+4.98+4=98.(4+98)+4
=98.102+4
=9996+4
=10000
b) x3 + 3x2 + 3x +1
Tại x=99 ta có:
993+3.(992)+3.99+1=992.(99+3)+3.99+1
=992.102+298
=999702+298
=1000000
Bài 4: Rút gọn các biểu thức sau:
a)A=(2x+y)2-(y-2x)2
b)B=x2-y2+(x-y)2
Rút gọn các biểu thức sau :
a) (a + b)2 – (a – b)2
b) (a + b)3 – (a – b)3 – 2b3
c) (x + y + z)2 – 2(x + y + z)(x + y) + (x + y)2
a) (a + b)2 – (a – b)2
= (a2 + 2ab + b2) – (a2 – 2ab + b2)
= a2 + 2ab + b2 – a2 + 2ab - b2
= 4ab
b) (a + b)3 – (a – b)3 – 2b3
= (a3 + 3a2b + 3ab2 + b3) – (a3 – 3a2b + 3ab2 – b3) – 2b3
= a3 + 3a2b + 3ab2 + b3 – a3 + 3a2b - 3ab2 + b3 – 2b3
= 6a2b
c) (x + y + z)2 – 2(x + y + z)(x + y) + (x + y)2
= x2 + y2 + z2+ 2xy + 2yz + 2xz – 2(x2 + xy + yx + y2 + zx + zy) + x2 + 2xy + y2
= 2x2 + 2y2 + z2 + 4xy + 2yz + 2xz – 2x2 – 4xy – 2y2 – 2xz – 2yz
= z2
Rút gọn các biểu thức sau :
a) \(\left(a+b\right)^2-\left(a-b\right)^2\)
b) \(\left(a+b\right)^3-\left(a-b\right)^3-2b^3\)
c) \(\left(x+y+z\right)^2-2\left(x+y+z\right)\left(x+y\right)+\left(x+y\right)^2\)
Bài giải:
a) (a + b)2 – (a – b)2 = (a2 + 2ab + b2) – (a2 – 2ab + b2)
= a2 + 2ab + b2 – a2 + 2ab - b2 = 4ab
Hoặc (a + b)2 – (a – b)2 = [(a + b) + (a – b)][(a + b) – (a – b)]
= (a + b + a – b)(a + b – a + b)
= 2a . 2b = 4ab
b) (a + b)3 – (a – b)3 – 2b3
= (a3 + 3a2b + 3ab2 + b3) – (a3 – 3a2b + 3ab2 – b3) – 2b3
= a3 + 3a2b + 3ab2 + b3 – a3 + 3a2b - 3ab2 + b3 – 2b3
= 6a2b
Hoặc (a + b)3 – (a – b)3 – 2b3 = [(a + b)3 – (a – b)3] – 2b3
= [(a + b) – (a – b)][(a + b)2 + (a + b)(a – b) + (a – b)2] – 2b3
= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2) – 2b3
= 2b . (3a2 + b2) – 2b3 = 6a2b + 2b3 – 2b3 = 6a2b
c) (x + y + z)2 – 2(x + y + z)(x + y) + (x + y)2
= x2 + y2 + z2+ 2xy + 2yz + 2xz – 2(x2 + xy + yx + y2 + zx + zy) + x2 + 2xy + y2
= 2x2 + 2y2 + z2 + 4xy + 2yz + 2xz – 2x2 – 4xy – 2y2 – 2xz – 2yz = z2
1. Rút gọn các biểu thức sau:
M = (2a+b)2-(b-2a)2
N = (3a+2)2+2a(1-2b)+(2b-1)2
A = (m-n)2+4mn
2. Tính:
a) (x+5)2 b) (5/2-t)2
c) (2u+3v)2 d) (-1/8 a+2/3 bc)2
e) (x/y-1/z)2 f) (mn/4-x/6)(mn/4+x/6)
Bài 2:
a) \(\left(x+5\right)^2=x^2+10x+25\)
b) \(\left(\dfrac{5}{2}-t\right)^2=\dfrac{25}{4}-5t+t^2\)
c) \(\left(2u+3v\right)^2=4u^2+12uv+9v^2\)
d) \(\left(-\dfrac{1}{8}a+\dfrac{2}{3}bc\right)^2=\dfrac{1}{64}a^2-\dfrac{1}{6}abc+\dfrac{4}{9}b^2c^2\)
e) \(\left(\dfrac{x}{y}-\dfrac{1}{z}\right)^2=\dfrac{x^2}{y^2}-\dfrac{2x}{yz}+\dfrac{1}{z^2}\)
f) \(\left(\dfrac{mn}{4}-\dfrac{x}{6}\right)\left(\dfrac{mn}{4}+\dfrac{x}{6}\right)=\dfrac{m^2n^2}{16}-\dfrac{x^2}{36}\)
Bài 1:
$M=(2a+b)^2-(b-2a)^2=[(2a+b)-(b-2a)][(2a+b)+(b-2a)]$
$=4a.2b=8ab$
$N=(3a+1)^2+2a(1-2b)+(2b-1)^2$
$=(9a^2+6a+1)+2a-4ab+(4b^2-4b+1)$
$=9a^2+8a+4b^2-4b-4ab+2$
$A=(m-n)^2+4mn=m^2-2mn+n^2+4mn$
$=m^2+2mn+n^2=(m+n)^2$
Bài 1:
a: Ta có: \(M=\left(2a+b\right)^2-\left(b-2a\right)^2\)
\(=4a^2+4ab+b^2-b^2+4ab-4a^2\)
\(=8ab\)
b: Ta có: \(N=\left(3a+2\right)^2+2a\left(1-2b\right)+\left(2b-1\right)^2\)
\(=\left(3a+2+1-2b\right)^2\)
\(=\left(3a-2b+3\right)^2\)
\(=9a^2+4b^2+9-12ab+18a-12b\)
c: Ta có: \(A=\left(m-n\right)^2+4nm\)
\(=m^2-2mn+n^2+4mn\)
\(=m^2+2mn+n^2\)
\(=\left(m+n\right)^2\)
2:
a: \(\left(x+5\right)^2=x^2+10x+25\)
b: \(\left(\dfrac{5}{2}-t\right)^2=\dfrac{25}{4}-5t+t^2\)