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.

Step-by-step explanation:

Given

Required

Find

Express 37 as 40 - 3

So, we have:

Compare to

Substitute 40 for x and 3 for y in

Evaluate all exponents

Evaluate all products

Hence:

70

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)