Use the identity a3+b3=(a+b)3−3ab(a+b) to determine the sum of the cubes of two numbers if the sum of the two numbers is 4 and the product of the two numbers is 1.

enter your answer as a number, like this: 42

= 52

Step-by-step explanation:

Using the equation;

a3+b3=(a+b)3−3ab(a+b)

The sum, a+b =4

The product, ab = 1

Therefore;

a3+b3=4³−3(1)(4)

         = 64-12

          = 52

a³+b³ = 52

Step-by-step explanation:

We have given that

The sum of two numbers is 4.

The product of two numbers is 1.

a+b = 4

ab= 1

We have to find the sum of the cubes of two numbers.

a³+b³ = ?

Using given identity, we have

a³+b³ = (a+b)³-3ab(a+b)

Putting given values in formula, we have

a³+b³ = (4)³-3(1)(4)

a³+b³ = 64-12

a³+b³ = 52 which is the answer.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.