Đáp án:
`a)` `f(x)+g(x)=5x^6+5x^5-6x^4+2x^3+2x^2-6x+11`
` f(x)-g(x)=x^6+15x^5-10x^4+10x^3-10x^2+10x-9`
`b)` `f(x)+g(x)=5x^4`
` f(x)-g(x)==x^4+30x^3+14x^2+6x^3-1`
Giải thích các bước giải:
`a)` Có `f(x)=3x^6+10x^5-8x^4+6x^3-4x^2+2x+1`
` g(x)=2x^6-5x^5+2x^4-4x^3+6x^2-8x+10`
`f(x)+g(x)`
`=(10x^5-8x^4+6x^3-4x^2+2x+1+3x^6)+(-5x^5+2x^4-4x^3+6x^2-8x+10+2x^6)`
`=3x^6+10x^5-8x^4+6x^3-4x^2+2x+1+2x^6-5x^5+2x^4-4x^3+6x^2-8x+10`
`=(3x^6+2x^6)+(10x^5-5x^5)+(2x^4-8x^4)+(6x^3-4x^3)+(6x^2-4x^2)+(2x-8x)+(1+10)`
`=5x^6+5x^5-6x^4+2x^3+2x^2-6x+11`
`f(x)-g(x)`
`=(3x^6+10x^5-8x^4+6x^3-4x^2+2x+1)-(2x^6-5x^5+2x`^4-4x^3+6x^2-8x+10)`
`=3x^6+10x^5-8x^4+6x^3-4x^2+2x+1-2x^6+5x^5-2x^4+4x^3-6x^2+8x-10`
`=(3x^6-2x^6)+(10x^5+5x^5)+(-8x^4-2x^4)+(6x^3+4x^3)+(-4x^2-6x^2)+(2x+8x)+(1-10)`
`=x^6+15x^5-10x^4+10x^3-10x^2+10x-9`
`b)` Có `f(x)=3x^4+15x^3+7x^2+3x-1/2`
` g(x)=2x^4-15x^3-7x^2-3x+1/2`
`f(x)+g(x)`
`=(3x^4+15x^3+7x^2+3x-1/2)+(2x^4-15x^3-7x^2-3x+1/2)`
`=3x^4+15x^3+7x^2+3x-1/2+2x^4-15x^3-7x^2-3x+1/2`
`=(3x^4+2x^4)+(15x^3-15x^3)+(7x^2-7x^2)+(3x-3x)+(1/2-1/2)`
`=5x^4`
`f(x)-g(x)`
`=(3x^4+15x^3+7x^2+3x-1/2)-(2x^4-15x^3-7x^2-3x+1/2)`
`=3x^4+15x^3+7x^2+3x-1/2-2x^4+15x^3+7x^2+3x-1/2`
`=(3x^4-2x^4)+(15x^3+15x^3)+(7x^2+7x^2)+(3x+3x)+(-1/2-1/2)`
`=x^4+30x^3+14x^2+6x^3-1`
