$\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{a^6+b^6}\implies a^{2\cdot 3}+b^{2\cdot 3}\implies (a^2)^3+(b^2)^3 \\[2em] [a^2+b^2] [(a^2)^2-a^2b^2+(b^2)^2]\implies \boxed{(a^2+b^2)(a^4-a^2b^2+b^4)}$

about the second one... well, is a "fait accompli" that using the pythagorean theorem, if x = 8 and y = 5, the hypotenuse must be √(8² + 5²) = √(89), which is neither of those choices.

5, 8, 13 are no dice, namely 5² + 8² ≠ 13

25, 64, 17 is are no dice too, because 25² + 17² ≠ 64²

however, 5,12 and 13 are indeed a pythagorean triple

also is 39, 80, 89.

when looking for a pythagorean triple, recall that c² = a² + b².

so the longest leg is the sum of the square of the small ones.

so what you'd do is, check the small legs, square them, add them up, if they're indeed a pythagorean triple, they "must" add up to the longest leg.

4 0

3 years ago

7x-3y=-6 convert to slope intercept form

r-ruslan [8.4K]

I think 7x-y=-2 is the answer

3 0

3 years ago

There are 18 pieces of chalk. The ratio if chalk that is yellow to chalk that is not yellow is 1:2. How many more pieces of whit

katen-ka-za [31]

The amount of chalk are equal

5 0

3 years ago

A group of 6 friends of varying ages meets at a coffee shop and sits in a circle. What is the probability that the

katrin2010 [14]

Answer:

1 out of 6

Step-by-step explanation:

So basically the shortest is one person in the group of six aand 1/6 cant be simplified so yeah

8 0

3 years ago

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