Toán lớp 8 :Tính
a. 5x(x^2-2x+3)
b.(x^2+1)(5-x)
c.(x-2)(x^2+3x-4)
d.(x-2)(x-x^2+4)
e.(x^2-1)(x^2+2x)
f.(2x-1)(3x+2)(3-x)
Toán lớp 8 :Tính
a. 5x(x^2-2x+3)
b.(x^2+1)(5-x)
c.(x-2)(x^2+3x-4)
d.(x-2)(x-x^2+4)
e.(x^2-1)(x^2+2x)
f.(2x-1)(3x+2)(3-x)
Giải thích các bước giải:
$\eqalign{ & a)\,5x({x^2} – 2x + 3) \cr & = 5{x^3} – 10{x^2} + 15x \cr & b)\,({x^2} + 1)(5 – x) \cr & = {x^2}(5 – x) + 1(5 – x) \cr & = 5{x^2} – {x^3} + 5 – x \cr & = – {x^3} + 5{x^2} – x + 5 \cr & c)\,(x – 2)({x^2} + 3x – 4) \cr & = x({x^2} + 3x – 4) – 2({x^2} + 3x – 4) \cr & = {x^3} + 3{x^2} – 4x – (2{x^2} + 6x – 8) \cr & = {x^3} + 3{x^2} – 4x – 2{x^2} – 6x + 8 \cr & = {x^3} + {x^2} – 10x + 8 \cr & d)\,(x – 2)(x – {x^2} + 4) \cr & = x(x – {x^2} + 4) – 2(x – {x^2} + 4) \cr & = {x^2} – {x^3} + 4x – 2x + {x^3} – 8 \cr & = {x^2} + 2x – 8 \cr & e)\,({x^2} – 1)({x^2} + 2x) \cr & = {x^2}({x^2} + 2x) – ({x^2} + 2x) \cr & = {x^4} + 2{x^3} – {x^2} – 2x \cr & f)\,\left( {2x – 1} \right)\left( {3x + 2} \right)\left( {3 – x} \right) \cr & = \left( {2x – 1} \right)(9x + 6 – 3{x^2} – 2x) \cr & = \left( {2x – 1} \right)( – 3{x^2} + 7x + 6) \cr & = 2x( – 3{x^2} + 7x + 6) – ( – 3{x^2} + 7x + 6) \cr & = – 6{x^3} + 14{x^2} + 12x + 3{x^2} – 7x – 6 \cr & = – 6{x^3} + 17{x^2} + 5x – 6 \cr} $