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a: \(-3x^2\cdot\left(\dfrac{4}{3}x^2+\dfrac{2}{3}x^2-\dfrac{1}{3}\right)\)
\(=-4x^4-2x^4+x^2\)
b: \(\left(x-3y\right)\left(3x^2+5xy+4y^2\right)\)
\(=3x^3+5x^2y+4xy^2-9x^2y-15xy^2-12y^3\)
\(=3x^3-4x^2y-11xy^2-12y^3\)
c: \(\left(x+8\right)^2-2\left(x+8\right)\left(x-2\right)+\left(x-2\right)^2\)
\(=\left(x+8-x+2\right)^2\)
\(=10^2=100\)
d: \(x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)
\(=x\left(x^2-16\right)-\left(x^2+1\right)\left(x^2-1\right)\)
\(=x^3-16x-x^4+1\)
a: \(=x^5+1-x^5+1=2\)
b: \(=\left(6b^3+2b^2-5b-2\right)\left(3b^2-b+3\right)\)
\(=18b^5-6b^4+18b^3+6b^4-2b^3+6b^2-15b^3+5b^2-15b-6b^2+2b-6\)
\(=18b^5+b^3+5b^2-13b-6\)
c: \(=\left(2a^2+2ab+b^2\right)\cdot2a\left(b^2+2a^2-2ab\right)\)
\(=2a\left[\left(2a^2+b^2\right)^2-4a^2b^2\right]\)
\(=2a\left(4a^4+b^4\right)=8a^5+2ab^4\)
a: \(=x^3-3x^2+3x-1-x^3-64+3x^2-3x\)
=-65
b \(=8x^3+27y^3-8x^3+27y^3-54y^3+27\)
=27
c: \(=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)=0\)
d: \(=x^3-3x^2+3x-1-x^3+1-3x\left(1-x\right)\)
\(=-3x^2+3x-3x+3x^2=0\)
a) \(\left(x+4\right)\left(x^2-4x+16\right)=x^3+4^3=x^3+64\)
b) \(\left(\frac{1}{3}x+2y\right)\left(\frac{1}{9}x^2-\frac{2}{3}xy+4y^2\right)=\left(\frac{1}{3}x\right)^3+\left(2y\right)^3=\frac{1}{27}x^3+8y^3\)
c) \(\left(x-3y\right)\left(x^2+3xy+9y^2\right)=x^3-\left(3y\right)^3=x^3-27y^3\)
d) \(\left(x^2-\frac{1}{3}\right)\left(x^4+\frac{1}{2}x^2+\frac{1}{9}\right)=\left(x^2\right)^3-\left(\frac{1}{3}\right)^3=x^6-\frac{1}{9}\)
( x + 4 )( x2 - 4x + 16 ) = x3 + 43 = x3 + 64
( 1/3x + 2y )( 1/9x2 - 2/3xy + 4y2 ) = ( 1/3x )3 - ( 2y )3 = 1/27x3 - 8y3
( x - 3y )( x2 + 3xy + 9y2 ) = x3 - ( 3y )3 = x3 - 27y3
( x2 - 1/3 )( x4 + 1/3x2 + 1/9 ) = ( x2 )3 - ( 1/3 )3 = x6 - 1/27
HĐT số 6 + 7 bạn nhé ^^
1,Thực hiện phép tính :
a, (x + 2)9 : (x + 2)6
=(x+2)9-6
=(x+2)3
b, (x - y) 4 : (x - 2)3
=(x-y)4-3
=x-y
c, ( x2+ 2x + 4)5 : (x2 + 2x + 4)
=(x2+2x+4)5-1
=(x2+2x+4)4
d, 2(x2 + 1)3 : 1/3(x2 + 1)
=(2÷1/3).[(x2+1)3÷(x2+1)]
=6(x2+1)2
e, 5 (x - y)5 : 5/6 (x - y)2
=(5÷5/6).[(x-y)5÷(x-y)2]
=6(x-y))3
Bài 3:
a: \(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-4\right)\left(x+4\right)=21\)
\(\Leftrightarrow x^3-27-x\left(x^2-16\right)=21\)
\(\Leftrightarrow x^3-27-x^3+16x=21\)
=>16x=48
hay x=3
b: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=4\)
\(\Leftrightarrow x^3+8-x^3-2x=4\)
=>-2x=4-8=-4
hay x=2