Giải SBT toán 7 tập 2: bài tập 8.1 trang 26

a.

• \(f(x) = {x^2} + 2{x^3} - 7{x^5} - 9 - 6{x^7} + {x^3} + {x^2} + {x^5} - 4{x^2} + 3{x^7}\)

\(=- 6{x^7}+ 3{x^7}- 7{x^5}+ {x^5}+ 2{x^3}+ {x^3}+ {x^2}+ {x^2}- 4{x^2}-9\)

\(=-3x^7-6x^5+3x^3-2x^2-9\)

\(=-9-2x^2+3x^3-6x^5-3x^7\)

• \(g(x) = {x^5} + 2{x^3} - 5{x^8} - {x^7} + {x^3} + 4{x^2} - 5{x^7} + {x^4} - 4{x^2} - {x^6} - 12\)

\(=-12+ 4{x^2}- 4{x^2}+ 2{x^3}+ {x^3}+ {x^4}+{x^5}- {x^6}- {x^7} - 5{x^7}- 5{x^8} \)

\(=-12+3x^3+x^4+x^5-x^6-6x^7-5x^8\)

• \(h(x) = x + 4{x^5} - 5{x^6} - {x^7} + 4{x^3} + {x^2} - 2{x^7} + {x^6} - 4{x^2} - 7{x^7} + x\)

\(=x+x+ {x^2}- 4{x^2}+ 4{x^3}+ 4{x^5}- 5{x^6}+ {x^6}- {x^7}- 2{x^7}- 7{x^7}\)

\(=2x-3x^2+ 4{x^3}+ 4{x^5}-4{x^6}-10x^7\)

b. 

$f (x) + g (x) - h (x)$

\(=-9-2x^2+3x^3-6x^5-3x^7-12+3x^3+x^4+x^5-x^6-6x^7-5x^8-(2x-3x^2+ 4{x^3}+ 4{x^5}-4{x^6}-10x^7)\)

\(=-9-12-2x^2+3x^3+3x^3+x^4-6x^5+x^5-x^6-3x^7-6x^7-5x^8-2x+3x^2- 4{x^3}- 4{x^5}+4{x^6}+10x^7\)

\(=-21-2x^2+6x^3+x^4-5x^5-x^6-9x^7-5x^8-2x+3x^2- 4{x^3}- 4{x^5}+4{x^6}+10x^7\)

\(=-21-2x-2x^2+3x^2+6x^3- 4{x^3}+x^4-5x^5- 4{x^5}-x^6+4{x^6}-9x^7+10x^7-5x^8\)

\(=-21-2x+x^2+2x^3+x^4-9x^5+3x^6+x^7-5x^8\)