1. khai triển
a) (a-b+c)2
b) (a+b-c-d)2
c) (2x - y + 3z)2
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Câu 3:
a: \(49^2=2401\)
b: \(51^2=2601\)
c: \(99\cdot100=9900\)
a) (x - 1/2x²y)²
= x² - 2x . 1/2 x²y + (1/2x²y)²
= x² - x³y + 1/4 x⁴y²
b) (2xy² - 1)(1 + 2xy²)
= (2xy²)² - 1²
= 4x²y⁴ - 1
c) (x - y + 2)²
= (x - y)² + 2(x - y).2 + 2²
= x² - 2xy + y² + 4x - 4y + 4
= x² + y² - 2xy + 4x - 4y + 4
d) (x + 1/2)(1/2 - x)
= (1/2)² - x²
= 1/4 - x²
e) (x² - 1/3)²
= (x²)² - 2x².1/3 + (1/3)²
= x⁴ - 2/3 x² + 1/9
a) \(\left(2x-3y\right)^2=4x^2-12xy+9y^2\)
b) \(\left(5p-q\right)^2=25p^2-10pq+q^2\)
c) \(\left(-a-b\right)^2=-a^2-2ab-b^2\)
d) \(\left(1+3s\right)^2=1+6s+9s^2\)
e) \(\left(a^2b+2b\right)^2=a^4b^2+4a^2b^2+4b^2\)
f) \(\left(3u-v\right)^3=27u^3-27u^2v+9uv^2-v^3\)
a,\(\left(2x-3y\right)=\left(2x\right)^2-2.2x.3y+\left(3y\right)^2\)
=\(4x^2-12xy+6y^2\)
b,\(\left(5p-q\right)^2=\left(5p\right)^2-2.5p.q+q^2\)
=\(25p^2-10pq+q^2\)
c,(-a-b)\(^2=\left(-a\right)^2-2.\left(-a\right).b+b^2\)
=\(a^2+2ab+b^2\)
d,\(\left(1+3s\right)^2=1+6s+9s^2\)
e,(a\(^2b+2b)^2=(a^2b)^2+2.a^2b.2b^2+\left(2b\right)^2\)
=\(a^4b^2+4a^2b^2+4b^2\)
f,\(\left(3u-v\right)^3=27u^3-27u^2v+9uv^2-v^3\)
5:
a: (2x-5)(2x+5)=4x^2-25
b: (3x-5y)(3x+5y)=9x^2-25y^2
c: (3x+7y)(3x-7y)=9x^2-49y^2
d: (2x-1)(2x+1)=4x^2-1
4:
a: 2003*2005=(2004-1)(2004+1)=2004^2-1<2004^2
b: 8(7^2+1)(7^4+1)(7^8+1)
=1/6*(7-1)(7+1)(7^2+1)(7^4+1)(7^8+1)
=1/6(7^2-1)(7^2+1)(7^4+1)(7^8+1)
=1/6(7^16-1)<7^16-1
5:
a: (2x-5)(2x+5)=4x^2-25
b: (3x-5y)(3x+5y)=9x^2-25y^2
c: (3x+7y)(3x-7y)=9x^2-49y^2
d: (2x-1)(2x+1)=4x^2-1
mik chỉ biết bài 5 thôi !
Đề này là Toán chứ nhỉ!?
a) (x + 1)3 = x3 + 3x2 + 3x + 1
b) (2x + 3)3 = 8x3 + 36x2 + 54x + 27
c) \(\left(x+\frac{1}{2}\right)^3=\) \(x^3+\frac{3x^2}{2}+\frac{3x}{4}+\frac{1}{8}\)
d) (x2 + 2)3 = x6 + 6x4 + 12x2 + 8
e) (2x + 3y)3 = 8x3 + 36x2y + 54xy2 + 27y3
f) \(\left(\frac{1}{2}x+y^2\right)^3=\frac{x^3}{8}+\frac{3x^2y^2}{4}+\frac{3xy^4}{2}+y^6\)
a) (x - 1)2 = x2 - 2x + 1
b) ( x + 2 )2 = x2 + 4x + 4
c) (y + 2a )2 = y2 + 4ya + 4a2
e) (2x - y)3 = ( 2x )3 - 3.(2x)2.y + 3.2x.y2 - y3 = 8x3 - 12x2y + 6xy2 - y3
g) (3a+6)3 = (3a)3 + 3.(3a)2.6 + 3.3a.62 + 63 = 27a3 + 162a2 + 324a + 216
\(a.\left(a-b+c\right)^2=a^2+b^2+c^2-2ab-2bc+2ca\)
\(b.\left(a+b-c-d\right)^2\)
\(=\left[a+b-\left(c+d\right)\right]\)
\(=a^2+b^2+\left(c+d\right)^2+2ab-2b\left(c+d\right)-2a\left(c+d\right)\)
\(=a^2+b^2+c^2+2cd+d^2+2ab-2bc-2bd-2ac-2ad\)
\(c.\left(2x-y+3z\right)^2=4x^2+y^2+9z^2-4xy-6yz+12xz\).