Khai triển tích 3(x-1)^2-(x+1)^3 Lm từng các một nha
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\(3\left(x-1\right)^2-\left(x+1\right)^2\)
\(=3x^2-6x+3-x^2-2x-1\)
\(=2x^2-8x+2\)
\(a,=x^3+3x^2+3x+1\\ b,=8x^3+36x^2+54x+27\\ c,=x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}\\ d,=x^6-6x^4+12x^2-8\\ e,=8x^3-36x^2y+54xy^2-27y^3\)
a.(x+3)(x+1)
=x.(x+1)+3.(x+1)
=x2+x+3x+3
=x2+4x+3
b.(x+6)(2x-2)
=x.(2x-2)+6.(2x-2)
=2x2-2x+12x-12
=2x2+10x-12
a) \(\left(\dfrac{1}{2}m+3\right)^3=\dfrac{m^3}{8}+\dfrac{9m^2}{4}+\dfrac{27m}{2}+9\)
b) \(2\left(m+\dfrac{1}{2}\right)=2m+1\)
c) \(\left(2\sqrt{x}+1\right)^2=4x+4\sqrt{x}+1\)
d) \(\left(2\sqrt{2}+\dfrac{1}{4}\right)^2=8+\sqrt{2}+\dfrac{1}{16}=\dfrac{129}{16}+\sqrt{2}\)
\(3x\left(x^2-5x+3\right)+\left(x+1\right)\left(x+2\right)\)
\(=3x^3-15x^2+9x+x^2+2x+x+2\)
\(=3x^3-14x^2+13x+2\)
a/ \(3x\left(x^2-5x+3\right)+\left(x+1\right)\left(x+2\right)\)
\(=3x^3-15x^2+9x+\left(x^2+2x+x+2\right)\)
\(=3x^3-15x^2+9x+x^2+2x+x+2\)
\(=3x^3-14x^2+13x+2\)
b/ \(\left(x+2\right)^2+\left(x-3\right)^2-\left(x-1\right)\left(x+1\right)\)
\(=\left(x^2+4x+4\right)+\left(x^2-6x+9\right)-\left(x^2-1\right)\)
\(=x^2+4x+4+x^2-6x+9-x^2+1\)
\(=x^2-2x+14x\)
\(C_n^0+C_n^1+C_n^2=11\)
\(\Rightarrow1+n+\dfrac{n\left(n-1\right)}{2}=11\)
\(\Leftrightarrow n^2+n-20=0\Rightarrow\left[{}\begin{matrix}n=4\\n=-5\left(loại\right)\end{matrix}\right.\)
\(\left(x^3+\dfrac{1}{x^2}\right)^4\) có SHTQ: \(C_4^k.x^{3k}.x^{-2\left(4-k\right)}=C_4^k.x^{5k-8}\)
\(5k-8=7\Rightarrow k=3\)
Hệ số: \(C_4^3=4\)
a) ( 3x + 5 )2 = 9x2+30x+25
b) ( x2- 4y )2 = x4 - 8x2y + 16y2
c) ( 8y+1 )( 8y-1 ) = 64y2 - 1
d) ( 2x3+1 ) = 8x9+6x6+6x3+1
e) 27y3 - 8 = ( 3y )3 - 23 = ( 3y -2 )( 9y2+6y+4 )
f)125 + 27y3 = 53 + ( 3y )3 = ( 5+3y )( 25+30y+9y2 )
Hk tốt
3(x - 1)2 - (x + 1)3
= 3(x2 - 2x + 1) - (x3 + 2x2 + 2x + 1)
= 3x2 - 6x + 3 - x3 - 2x2 - 2x - 1
= 3x2 - 2x2 - 6x - 2x - x3 + 3 - 1
= x2 - 8x - x3 + 2
Cảm ưn ạ