1. Nhân đa thức với đa thức:
a) ( 0,4x^3 – 3x^2 + 1 – x) * ( 0,2x^4 + 5x^2 – 4)
b) ( x^2 – 3x + 21) * ( -5x^3 +5/3 x^2 – x+3)
c) ( 3x^2y + 2,5y^2x ) * ( -1/2 x^2 – 3x -2/5 y^2)
d) ( -5x^3y^3 + 0,2x^2 – 3,2y^2 ) * ( -5x^2y^3 – 0,2y)
( Giúp mình )
Đáp án:
$a)
0,08x^7+1,8x^5-6,6x^3-0,6x^6-15x^4+17x^2+0,2x^4-4+4x\\
b)
-5x^5+\dfrac{50}{3}x^4 -111x^3+41x^2-30x+63\\
c)
\dfrac{-3}{2}x^4y-9x^3y-\dfrac{6}{5}x^2y^3+\dfrac{-5}{4}x^3y^2-\dfrac{15}{2}x^2y^2-xy^4\\
d)
25x^5y^6+x^3y^4-x^4y^3-0,04x^2y+16x^2y^5-0,64y^3$
Giải thích các bước giải:
$a)
(0,4x^3-3x^2+1-x).(0,2x^4+5x^2-4)\\
=0,4x^3.(0,2x^4+5x^2-4)-3x^2.(0,2x^4+5x^2-4)+1.(0,2x^4+5x^2-4)-x.(0,2x^4+5x^2-4)\\
=0,08x^7+2x^5-1,6x^3-0,6x^6-15x^4+12x^2+0,2x^4+5x^2-4-0,2x^5-5x^3+4x\\
=0,08x^7+(2x^5-0,2x^5)+(-1,6x^3-5x^3)-0,6x^6-15x^4+(12x^2+5x^2)+0,2x^4-4+4x\\
=0,08x^7+1,8x^5-6,6x^3-0,6x^6-15x^4+17x^2+0,2x^4-4+4x\\
b)
(x^2-3x+21).(-5x^3+\dfrac{5}{3}x^2-x+3)\\
=x^2.(-5x^3+\dfrac{5}{3}x^2-x+3)-3x.(-5x^3+\dfrac{5}{3}x^2-x+3)+21.(-5x^3+\dfrac{5}{3}x^2-x+3)\\
=-5x^5+\dfrac{5}{3}x^4-x^3+3x^2+15x^4-3x.\dfrac{5}{3}x^2+3x^2-9x-105x^3+21.\dfrac{5}{3}x^2-21x+63\\
=-5x^5+\dfrac{5}{3}x^4-x^3+3x^2+15x^4-5x^3+3x^2-9x-105x^3+35x^2-21x+63\\
=-5x^5+\left (\dfrac{5}{3}x^4 +15x^4 \right )+(-x^3-5x^3-105x^3)+(3x^2+3x^2+35x^2)+(-9x-21x)+63\\
=-5x^5+\dfrac{50}{3}x^4 -111x^3+41x^2-30x+63\\
c)
\left ( 3x^2y+2,5y^2x \right ).\left ( \dfrac{-1}{2}x^2-3x-\dfrac{2}{5}y^2 \right )\\
=3x^2y.\left ( \dfrac{-1}{2}x^2-3x-\dfrac{2}{5}y^2 \right )+2,5xy^2.\left ( \dfrac{-1}{2}x^2-3x-\dfrac{2}{5}y^2 \right )\\
=3x^2y.\dfrac{-1}{2}x^2-3x^2y.3x-3x^2y.\dfrac{2}{5}y^2+2,5xy^2.\dfrac{-1}{2}x^2-2,5xy^2.3x-2,5xy^2.\dfrac{2}{5}y^2\\
=\dfrac{-3}{2}x^4y-9x^3y-\dfrac{6}{5}x^2y^3+\dfrac{-5}{4}x^3y^2-\dfrac{15}{2}x^2y^2-xy^4\\
d)
(-5x^3y^3+0,2x^2-3,2y^2).(-5x^2y^3-0,2y)\\
=-5x^3y^3.(-5x^2y^3-0,2y)+0,2x^2.(-5x^2y^3-0,2y)-3,2y^2.(-5x^2y^3-0,2y)\\
=25x^5y^6+x^3y^4-x^4y^3-0,04x^2y+16x^2y^5-0,64y^3$