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\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)=8x^3+y^3\)
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\(A=\dfrac{1}{x^2+x}+\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x+3}\) (ĐK: \(x\ne-1;x\ne0;x\ne-2;x\ne-3\))
\(A=\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{x+3}\)
\(A=\dfrac{\left(x+2\right)\left(x+3\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\dfrac{x\left(x+3\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\dfrac{x\left(x+1\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}+\dfrac{x\left(x+1\right)\left(x+2\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)\(A=\dfrac{x^2+5x+6+x^2+3x+x^2+x+x^3+2x^2+x^2+2x}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
\(A=\dfrac{x^3+6x^2+11x+6}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
\(A=\dfrac{x^3+5x^2+6x+x^2+5x+6}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
\(A=\dfrac{x\left(x+5x+6\right)+\left(x^2+5x+6\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
\(A=\dfrac{\left(x^2+5x+6\right)\left(x+1\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
\(A=\dfrac{\left(x+1\right)\left(x+2\right)\left(x+3\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}\)
\(A=\dfrac{1}{x}\)
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Ta có:(a2+ab+b2)(a2-ab+b2)-(a4+b4)
= (a2+b2)2-a2b2-a4-b4=a4+2a2b2+b4-a2b2-a4-b4=a2b2
Ta có:(a2+ab+b2)(a2-ab+b2)-(a4+b4)
= (a2+b2)2-a2b2-a4-b4=a4+2a2b2+b4-a2b2-a4-b4=a2b2
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b: \(\left(x-1\right)\left(x+7\right)-x^2+3x\)
\(=x^2+6x-7-x^2+3x\)
=9x-7
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\(\left(\dfrac{1}{3}y+3\right)^3=\dfrac{1}{27}y^3+y^2+9y+27\)
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\(\left(\dfrac{1}{3y+3}\right)^3=\dfrac{1}{\left(3y+3\right)^3}=\dfrac{1}{27y^3+81y^2+81y+27}\)
\(\left(\dfrac{1}{3y+3}\right)^3=\dfrac{1^3}{\left(3y+3\right)^3}=\dfrac{1}{27\left(y^3+3y^2+3y+1\right)}\)
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a.ta có
\(\left(x+3\right)^3+\left(x^2+1\right)\left(x-2\right)=x^3+9x^2+27x+27+x^3-2x^2+x-2\)
\(=2x^3+7x^2+28x+25\)
b.\(\left(2x-1\right)^2-\left(2-x\right)^3=4x^2-4x+1+x^3-6x^2+12x-8\)
\(=x^3-2x^2+8x-7\)
a) (x + 3)3 + (x2 + 1)(x - 2)
= x3 + 9x2 + 27x + 27 + x3 - 2x + x - 2
= x3 + x3 + 9x2 + 27x - 2x + x + 27 - 2
= 2x3 + 9x2 + 26x + 25
b) (2x - 1)2 - (2 - x)3
= 4x2 - 4x + 1 - ( 8 - 12x + 6x2 - x3)
= 4x2 - 4x + 1 - 8 + 12x - 6x2 + x3
= x3 + 4x2 - 6x2 + 12x - 4x + 1 - 8
= x3 - 2x2 + 8x - 7
c: Ta có: \(6x^2-\left(2x+5\right)\left(3x-2\right)\)
\(=6x^2-6x^2+4x-15x+10\)
=-11x+10
d: Ta có: \(2x\left(3x-1\right)-\left(x-3\right)\left(6x+2\right)\)
\(=6x^2-2x-6x^2-2x+18x+6\)
=14x+6