I NEED HELP ASAP THIS IS MY LAST ASSIGNMENT AND IF I DON'T GET THIS DONE I WILL FAIL

Polynomial Identities

Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.

Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.

I HAVE 45 = 50 - 5

Part 1 is explained in 1) of the explanation.

Part 2 is explained in 2) of the explanation.

Step-by-step explanation:

1) So you choose 45 and to write it as 50-5.

We want to square 45 without using a calculator.

That is we want to find without a calculator.

by your identity .

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2) Choose two numbers for and between 8 and 15. I will choose 10 and 12 .

Now we have to multiply 22 and 124 without a calculator...

22(124)

(20+2)(124)

124(20)+124(2)

124(10+10)+124(2)

1240+1240+248

2480+248

2728

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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what do u need to know

step-by-step explanation: