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Serga [27]
2 years ago
14

Find the value of 373 using the identity (x − y)3 = x3 − 3x2y + 3xy2 − y3. Show all work.

Mathematics
1 answer:
Paladinen [302]2 years ago
7 0

Answer:

37^3 = 50653

Step-by-step explanation:

Given

(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

Required

Find 37^3

Express 37 as 40 - 3

So, we have:

37^3 = (40 - 3)^3

Compare to (x -y)^3

x = 40\ and\ y = 3

Substitute 40 for x and 3 for y in (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

(40 - 3)^3 = 40^3 - 3*40^2*3 + 3*40*3^2 - 3^3

Evaluate all exponents

(40 - 3)^3 = 64000 - 3*1600*3 + 3*40*9 - 27

Evaluate all products

(40 - 3)^3 = 64000 - 14400 + 1080 - 27

(40 - 3)^3 = 50653

Hence:

37^3 = 50653

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