Bài 4:
\(a.x^3+y^3\\ =\left(x+y\right)^3-3x^2y-3xy^2\\ =\left(x+y\right)^3-3xy\left(x+y\right)\\ =1^3-3\cdot\left(-1\right)\cdot1\\ =1+3\\ =4\\ b.x^3-y^3\\ =\left(x-y\right)\left(x^2+xy+y^2\right)\\ =\left(x-y\right)\left[\left(x-y\right)^2+3xy\right]\\ =\left(x-y\right)^3+3xy\left(x-y\right)\\ =1^3+3\cdot6\cdot1\\ =1+18\\ =19\)
Bài 2:
a: \(A=\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\)
\(=x^3+1^3-\left(x^3-1^3\right)\)
\(=x^3+1-x^3+1=2\)
b: \(B=\left(2x+6\right)\left(4x^2-12x+36\right)-8x^3+10\)
\(=\left(2x+6\right)\left[\left(2x\right)^2-2x\cdot6+6^2\right]-8x^3+10\)
\(=8x^3+216-8x^3+10=226\)
c: \(C=\left(x-1\right)^3-\left(x-3\right)\left(x^2+3x+9\right)-3x\left(1-x\right)\)
\(=x^3-3x^2+3x-1-\left(x^3-27\right)-3x+3x^2\)
\(=x^3-1-x^3+27=26\)
Bài 3:
a: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x+3\right)\left(x-3\right)=26\)
=>\(x^3+2^3-x\left(x^2-9\right)=26\)
=>\(x^3+8-x^3+9x=26\)
=>9x=26-8=18
=>\(x=\dfrac{18}{9}=2\)
b: \(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-4\right)\left(x+4\right)=21\)
=>\(x^3-3^3-x\left(x^2-16\right)=21\)
=>\(x^3-27-x^3+16x=21\)
=>16x-27=21
=>16x=27+21=48
=>\(x=\dfrac{48}{16}=3\)
c: \(\left(2x-1\right)\left(4x^2+x+1\right)-4x\left(2x^2-3\right)=23\)
=>\(8x^3-1-8x^3+12x=23\)
=>12x-1=23
=>12x=23+1=24
=>x=2
