Bài `1:`
`a)`
`A = (x+y)^2- (x-y)^2`
`= [ (x+y) - (x-y)] . [ (x+y) + (x-y)]`
`= (x+y-x+y)(x+y+x-y)`
`= 2x . 2y`
`= 4xy`
Vậy `A = 4xy`
`b)`
`B = (x+y)^2 - 2 (x+y) (x-y) + (x-y)^2`
`= [(x+y) - (x-y)]^2`
`= (x + y - x + y)^2`
`= (2y)^2`
`= 4y^2`
Vậy `B = 4y^2`
`c)`
`C = x^2 (x-4) (x+4) - (x^2 + 1)(x^2 -1)`
` = x^2 (x^2 - 4^2) - [ (x^2)^2 - 1^2]`
` = x^2 (x^2 - 16) - (x^4 - 1)`
` = x^4 - 16x^2 - x^4 + 1`
` = 1 - 16x^2`
Vậy `C = 1 - 16x^2`
`d)`
`D = (y-3)(y+3)(y^2+9) - (y^2+2)(y^2-2)`
` = (y^2 - 3^2)(y^2+9) - [ (y^2)^2 - 2^2]`
`= (y^2- 9)(y^2+9) - (y^4 - 4)`
` = [(y^2)^2 - 9^2] - (y^4 - 4)`
`= (y^4 - 81) - (y^4-4)`
`= y^4 - 81- y^4 + 4`
` = -77`
Vậy `D = -77`
`e)`
`E = (x-y+z)^2 + (z-y)^2 + 2 (x-y+z)(y-z)`
` = (x-y+z)^2 + (y-z)^2 + 2 (x-y+z)(y-z)`
` = [ (x-y+z) + (y-z)]^2`
`= (x - y + z + y - z )^2`
` = x^2`
Vậy `E = x^2`
Bài `2:`
`a)`
`x^2 + 20x + 100 = (x + 10)^2`
`b)`
`y^2 - 14y + 49 = (y-7)^2`
`c)`
`16x^2 + 24xy + 9y^2 = (4x + 3y)^2`
`d)`
` 9x^2 - 42xy + 49y^2 = (3x - 7y)^2`
