Đáp án:
`a)4x²`
`b)6a²+3b²+2c²`
`c)-y²`
`d)x^8-16`
Giải thích các bước giải:
`a)(2x+3y+4)²+(3y+4)²-2.(2x+3y+4).(3y+4)`
`=(2x+3y+4)²-2.(2x+3y+4).(3y+4)+(3y+4)²`
`=[(2x+3y+4)-(3y+4)]²`
`=(2x+3y+4-3y-4)²`
`=(2x)²`
`=4x²`
`b)(a+b+c)²+(a+b-c)²+(2a-b)²`
`=[(a+b)+c]²+[(a+b)-c]²+4a²-4ab+b²`
`=(a+b)²+2c(a+b)+c²+(a+b)²-2c(a+b)+c²+4a²-4ab+b²`
`=a²+2ab+b²+2ac+2bc+c²+a²+2ab+b²-2ac-2bc+c²+4a²-4ab+b²`
`=(a²+a²+4a²)+(2ab+2ab-4ab)+(b²+b²+b²)+(2ac-2ac)+(2bc-2bc)+(c²+c²)`
`=6a²+3b²+2c²`
`c)(5x+y-3)(5x-y-3)-(5x-3)²`
`=[(5x-3)+y][(5x-3)-y]-(5x-3)²`
`=(5x-3)²-y²-(5x-3)²`
`=-y²`
`d)(x²-2x+2)(x²-2)(x²+2x+2)(x²+2)`
`=[(x²-2)(x²+2)][(x²-2x+2)(x²+2x+2)]`
`=[(x^2)^2-2^2][(x²+2)^2-(2x)^2]`
`=(x^4-4)(x^4+4x²+4-4x²)`
`=(x^4-4)(x^4+4)`
`=(x^4)^2-4^2`
`=x^8-16`
