Question

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


Hint: 373 = (40 − 3)3; therefore, x = 40 and y = 3.

Answer 1

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:

$37^3 = 50653$