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\(a.\left(a-b+c\right)^2=a^2+b^2+c^2-2ab-2bc+2ca\)
\(b.\left(a+b-c-d\right)^2\)
\(=\left[a+b-\left(c+d\right)\right]\)
\(=a^2+b^2+\left(c+d\right)^2+2ab-2b\left(c+d\right)-2a\left(c+d\right)\)
\(=a^2+b^2+c^2+2cd+d^2+2ab-2bc-2bd-2ac-2ad\)
\(c.\left(2x-y+3z\right)^2=4x^2+y^2+9z^2-4xy-6yz+12xz\).
Bài 6: Khai triển các biểu thức sau
a. C = ( x-y+z)2
=x2+y2+z2-2xy+2xz-2yz
b. D = (a+1-2b)2
=a2+12+(2b)2+2.a.1-2.a.2b+2.1.2b
=a2+1+4b2+2a-4ab+4b
Bài 7: Tính nhanh
a. 312=(30+1)2=302+2.30.1+12
=900+60+1
=961
b. 992
=(100-1)2
=1002-2.100.1+12
=10000-200+1
=10201
c. 62.58
=(60-2).(60+2)
=602-22
=3600-4
=3596
Bài 6:
a. C = \(\left(x-y+z\right)^2\)
C = \(x^2\) + \(y^2\) + \(z^2\) - 2xy + 2xz - 2yz
b. D = \(\left(a+1-2b\right)^2\)
D = \(a^2\) + 1 + \(4b^2\) + 2a - 4ab - b
Bài 7:
a. \(31^2\)
= \(\left(30+1\right)^2\)
= \(30^2\) + 2.30.1 + 1
= 900 + 60 +1
= 961
b. \(\left(100-1\right)^2\)
= \(100^2\) - 2.100.1 +1
= 10000 - 200 + 1
= 9801
c. 62.58
= (60 + 2).(60 - 2)
= \(60^2\) - \(2^2\)
= 3600 - 4
= 3596
a, Ta có : \(\left(3a+2b\right)^3\)\(=27a^3+54a^2b+36ab^2+8b^3\)
b, Ta có : \(\left(4x-y^2\right)^3=64x^3-48x^2y^2+12xy^4-y^6\)
a. (x + y)2 = x2 + 2xy + y2
b. (x - 2y)2 = x2 - 4xy - 4x2
c. (xy2 + 1)(xy2 - 1) = x2y4 - 1
d. (x + y)2(x - y)2 = (x2 + 2xy + y2)(x2 - 2xy + y2) = x4 - (2xy + y2)2 = x4 - (4x2y2 + y4) = x4 - 4x2y2 - y4
1) (a+2b+1)\(^2\)
=a\(^2\)+2a(2b+1)+(2b+1)2
=a2+4ab+2a+(2b)2+2.2b.1+12
=a2+4ab+2a+4b2+4b+1
2) (2a-b+3)2
=(2a)2 -2.2a(b-3)+(b-3)2
=4a2-4a(b-3)+b2-2b.3+32
=4a2-4ab+12a+b2 -6b+9
3) (2a-3b+1)2
=(2a)2-2.2a(3b-1)+(3b-1)2
=4a2-4a(3b-1)+(3b)2-2.3b.1+12
=4a2-4ab+4a+9b2-6b+1
1a. \(\left(2-3x\right)^2=4-12x+9x^2=9x^2-12x+4\)
\(b.\left(x-4\right)\left(x+4\right)=x^2-16\)
\(c.\left(x-1\right)^2-\left(x+2\right)^2=\left(x-1+x+2\right)\left(x-1-x-2\right)=\left(2x+1\right)\left(-3\right)=-6x-3\)
2. a) \(A=x^2-14x=x^2-2.7.x+7^2-49=\left(x-7\right)^2-49\)
\(b.B=\dfrac{1}{4}x^2+x=\dfrac{1}{4}\left(x^2+4x\right)=\dfrac{1}{4} \left(x^2+2x.2+2^2-4\right)=\dfrac{1}{4}\left[\left(x+2\right)^2-4\right]=\dfrac{1}{4}\left(x+2\right)^2-1\)
c.d Tương tự
Bài 1: Khai triển các hằng đẳng thức
a) ( x - 3 )( x2 + 3x + 9 )
= x3 - 33
= x3 - 27
b) ( 5x - 1 )( 1 + 5x + 25x2 )
= ( 5x - 1 )(25x2 + 5x + 1 )
= (5x)3 - 1
= 125x3 - 1
c) ( x2 - 1 ) ( x4 + x2 + 1 )
= (x2)3 - 1
= x6 - 1
a) ( x - 3 )( x2 + 3x + 9 )=x3-9
b) ( 5x - 1 ) ( 1 + 5x + 25x2 )=125x3-1
c) ( x2 - 1 ) ( x4 + x2 + 1 )=x6-1
a) ( a - b + c ) 2 = a2 + b2 + c2 + 2ab - 2ac - 2bc
b ) ( a - b - c )2 = a² + b² + c² - 2ab + 2bc - 2ca
Giải
a/\(\left(a-b+c\right)^2=a^2+b^2+c^2+2ab-2ac-2bc\)
b/\(\left(a-b-c\right)^2=a^2+b^2+c^2-2ab+2bc-2ca\)