Use the identity
a3+b3=(a+b)3−3ab(a+b)a3+b3=(a+b)3−3 ab(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

The sum of the cubes of two numbers is 52

Explanation:

Let a and b be two numbers.

It is given that the sum of the two numbers is 4 and the product of the two numbers is 1

Thus, Rewriting it in the expression form, we have,

To determine the sum of the cubes of two numbers, let us substitute these values in the identity , we get,

Thus, the sum of the cubes of two numbers is 52

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

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