Bài 1:
`a)`
`(3x+y^2)^2`
`=(3x)^2+2.3x.y^2+(y^2)^2`
`=9x^2+6xy^2+y^4`
Áp dụng: `(A+B)^2=A^2+2AB+B^2`
`b)`
`(1/2x+y)^3`
`=(1/2x)^3+ 3 . (1/2x)^2 . y+3 . 1/2x . y^2+y^3`
`=1/8x^3+3/4x^2y+3/2xy^2+y^3`
Áp dụng: `(A+B)^3=A^3+3A^B+3AB^2+B^3`
`c)`
`(xy-3)^3`
`=(xy)^3-3.(xy)^2 . 3+3.xy.3^2-3^3`
`=x^3y^3-9x^2y^2+27xy-27`
Áp dụng: `(A-B)^3=A^3-3A^B+3AB^2-B^3`
`d)`
`70^2-30^2`
`=(70-30)(70+30)`
`=40.100`
`=4000`
Áp dụng: `A^2-B^2=(A-B)(A+B)`
Bài 2:
`a)`
`4x^4-24x^2+36`
`=(2x^2)^2-2.2x^2 . 6+6^2`
`=(2x^2-6)^2`
Áp dụng: `A^2+2AB+B^2=(A+B)^2`
`b)`
`x^6-3/2x^2y+3/4x^2y^2-1/8y^3`
`=(x^2)^3 - 3 . x^2 . 1/2y +3.x^2 . (1/2y)^2-(1/2y)^3`
`=(x^2-1/2y)^3`
Áp dụng: `A^3-3A^2B+3AB^2-B^3=(A-B)^3`
`c)`
`-4x^2+4x-1`
`=-(4x^2-4x+1)`
`=-[(2x)^2-2.2x . 1+1^2]`
`=-(2x-1)^2`
Áp dụng: `A^2-2AB+B^2=(A-B)^2`
