b. 2( -3 - 2)² - 4( -6 / 3)² + 8( -1)⁴
=2(-5)²-4(-2)²+8(-1)⁴
=2(25)-4(4)+8(1)
=50-16+8
=42
edits:
LCM= lowest common multiple= lowest number with certain numbers as factors
multiple= number with certain numbers as factors eg. 8 is a multiple of 2 b/c 2x4=8
factors= numbers when multiplied to make the answer e.g 8. factors= 1,2,4,8 => 1x8=8 2x4=8
2. see definition of LCM and multiple
3. see definition of multiple and apply
4. To find when the planets line up, you must find when they meet. This means you must find a multiple of all 3 numbers (the amount of orbits for each planet). A multiple can easily be found by multiplying the numbers together. To find how many years it'll take, it is implying the least amount of time so you must find the lowest common multiple. This can by found by dividing the initial answer you got, from multiplying the numbers, by 2. When you divide, check to see if the new number can be divisible by the original 3 numbers. If they can, then this number is a lower common multiple, if it cant, then the original number is the lowest. Keep dividing by 2 until the resulting number can not be divided by the orbit numbers. The lowest number that works,60, is the answer
6. Find factors of the length and width of the board. The largest factor for both the length and the width is the answer. They must be the same factors because the tiles are squares so they must fit evenly both width and length.