Question

A) 5x(x-2)-x(5x-2)2=
d) (x-3)(x+3)-(x-2)²≤19=

Answer 1

A)5x(x-2)-x(5x-2)2 = (5x²-10x)(5x²+2x)2 = (5x²-10x)(10x²+4x) = 50x⁴+20x³-100x³-40x² = 50x⁴+80x³-40x²
d)(x-3)(x+3)-(x-2)²≤19
x²-9-(x²-4x+4)≤19
x²-9-x²+4x-4≤19
-13+4x≤19 |+13
4x≤32 |:4
x≤8

Answer 2

A) 5x(x-2) - x(5 -2)² = 5x² - 10x -x(25x² -20x+4)=
=5x² -10 x -25x³+20x² -4x= 25x³+25x² -14x

b) (x-3)(x+3)-(x-2)²≤19
x² - 9-(x² - 4x+4)≤ 19
x² -9-x² + 4x - 4≤19
4x ≤19+13
4x≤32 //:4
x ≤ 8