Question

Выражение a) (y-2)(y+3)(y-1)^2 b) 4(a+5)^2(4a^2+40a)

Answer 1

$(yy+y*3-2y-2*3)(y-1)^2$
$(y^2+3y-2y-6)(y-1)^2$
$(y^2+y-6)(y-1)^2$
$(y^2+y-6)((y-1)(y-1))$
$(y^2+y-6)(yy+y*-1-1y-1*-1)$
$(y^2+y-6)(y^2+2y+1)$
$y^2y^2+y^2(-2y)+y^2*1+(yy^2+y(-2y)+y*1)$
...$+(-6y^2-6(-2y)-6*1)$
$y^4-y^3-7y^2+13y-6$

$4((a+5)(a+5))(4a^2+40a)$
$4(aa+a*5+5a+5*5)(4a^2+40a)$
$4(a^2+5a+5a+25)(4a^2+40a)$
$4(a^2+10a+25)(4a^2+40a)$
$(4a^2+4(10a)+4*25)(4a^2+40a)$
$4a^2(4a^2)+4a^2(40a)+(40a(4a^2)+40a(40a))+(100(4a^2)+100(40a))$
$16a^4+320a^3+2000a^2+4000a$

Answer 2

A) (y-2)(y+3)(y-1)²= (y²-2y+3y-6)(y²+1-2y)= (y²+y-6)(y²+1-2y)= y⁴+y²-2y³+y³+y-2y²-6y²-6+12y= y⁴-y³-7y²+13y-6
b) 4(a+5)²(4a²+40)= (16a²+160)(a²+10a+25)= 16a⁴+160a³+400a²+160a²+1600a+4000=16a⁴+160a³+560a²+1600a+
4000