a: Ta có: \(A=\left(2x+y\right)^2-\left(2x-y\right)^2\)

\(=\left(2x+y-2x+y\right)\left(2x+y+2x-y\right)\)

\(=4x\cdot2y=8xy\)

b: Ta có: \(B=\left(3x+2\right)^2+2\left(3x+2\right)\left(1-2y\right)+\left(2y-1\right)^2\)

\(=\left(3x+2+1-2y\right)^2\)

\(=\left(3x-2y+3\right)^2\)

\((2x+y) (4x^2-2xy+y^2)-(3x-y)(9x^2+3xy+y^2) =8x^3+y^3-9x^3+y^3=17x^3\)

\(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)

\(=\left(2x+y\right)\left[\left(2x\right)^2-2xy+y^2\right]-\left(3x-y\right)\left[\left(3x\right)^2+3xy+y^2\right]\)

\(=\left(2x\right)^3+y^3-\left[\left(3x\right)^3-y^3\right]\)

\(=8x^3+y^3-27x^3+y^3\)

\(=-19x^3+2y^3\)

b: Ta có: \(\left(4x-y\right)\left(4x+y\right)-2\left(3x-2y\right)^2+\left(x-3y\right)^2\)

\(=16x^2-y^2-2\left(9x^2-12xy+4y^2\right)+x^2-6xy+9y^2\)

\(=17x^2-6xy+8y^2-18x^2+24xy-8y^2\)

\(=-x^2+18xy\)

c: Ta có: \(\left(2a-3b+4c\right)\left(2a-3b-4c\right)\)

\(=\left(2a-3b\right)^2-16c^2\)

\(=4a^2-12ab+9b^2-16c^2\)

a) \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=24-11x\)

b) \(\left(4x^2-3y\right)\cdot2y-\left(3x^2-4y\right)\cdot3y\)

\(=8x^2y-6y^2-9x^2y+12y^2\)

\(=6y^2-x^2y\)

c) \(3y^2\left[\left(2x-1\right)+y+1\right]-y\left(1-y-y^2\right)+y\)

\(=3y^2\cdot\left(2x-1+y+1\right)-y\cdot\left(1-y-y^2\right)+y\)

\(=6xy^2-3y^2+3y^3+3y^2-y+y^2+y^3+y\)

\(=4y^3+y^2+6xy^2\)

\(\left(x+y\right)^2+\left(x-y\right)^2+\left(x-y\right)\left(x+y\right)-3x^2\)

\(=\left(x^2+2xy+y^2\right)+\left(x^2-2xy+y^2\right)+\left(x^2-y^2\right)-3x^2\)

\(=x^2+2xy+y^2+x^2-2xy+y^2+x^2-y^2-3x^2\)

\(=3x^2+y^2-3x^2\)

\(=y^2\)

t

a: \(=\dfrac{\left(x+y\right)^3}{2\left(x+y\right)^2}=\dfrac{x+y}{2}\)

b: \(=\dfrac{x^2\left(3x-5\right)+3\left(3x-5\right)}{3x-5}=x^2+3\)

\(a,\left(3x+5\right)^2+\left(3x-5\right)^2-\left(3x+2\right)\left(3x-2\right)=9x^2+30x+25+9x^2-30x+25-9x^2+4=9x^2+54\)
\(b,BT=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x=x^3-16x^2+25x\)
\(c,BT=\left(x+y-z\right)^2-2\left(x+y-z\right)\left(x+y\right)+\left(x+y\right)^2=\left(x+y-z-x-y\right)^2=z^2\)

=-8y³+6xy²-9x²y+27x³

P/s:chả bít thu gọn hay kéo dài nó ra nx =.="