Answer:
1a.2.5x³-2.25x²+3.5x-1.5
1b.No, they aren't equal. (worked out the product for both and they weren't equal, see below)
2a.-2x⁶+7x⁴+3x³-3x²+11x+20
2b.Yes. When multiplying, it doesn't matter which term/expression you put first
3. The equation has two solutions: x=-2, x=3
Step-by-step explanation:
1. (a)
(0.5x-0.25)(5x²-2x+6)
0.5x(5x²-2x+6)-0.25(5x²-2x+6)
2.5x³-x²+3x -1.25x²+0.5x-1.5
2.5x³-2.25x²+3.5x-1.5
(b)
(0.25x-0.5)(5x²-2x+6)
0.25x(5x²-2x+6)-0.5(5x²-2x+6)
1.25x³-0.5x²+1.5x -2.5x²+x-3
1.25x³-3x²+2.5x-3
This is not equal to our answer for 1(a), so we can see they're not the same.
2(a)
(-2x³+x-5)(x³-3x-4)
-2x³(x³-3x-4) +x(x³-3x-4) -5(x³-3x-4)
-2x⁶+6x⁴+8x³ +x⁴-3x²-4x -5x³+15x+20
-2x⁶+7x⁴+3x³-3x²+11x+20
(b)
Yes. When multiplying, it doesn't matter which term/expression you put first: xy=yx. For example, 2(3)=6 and 3(2)=6.
3
2x²-2x-12=0
(divide each term by 2)
x²-x-6=0
(x+2)(x-3)=0
Anything multiplies by zero is zero, so either x+2=0 or x-3=0
If x+2=0, x=-2. If x-3=0, x=3.
The equation has two solutions: x=-2, x=3
is the first term of the series,
is the common ratio of the series, and
is the number of terms in this series.
